Here are the relevant paragraphs from the intro to the paywalled paper justifying the first line of the abstract:
Over the years however, it has been acknowledged that right-wing
authoritarianism is only one indicator of right-wing attitudes
and that such attitudes can be arranged according to two
broad dimensions (see, Duckitt & Sibley, 2009; Lipset, 1981).
The first dimension—social-cultural attitudes—relates to traditionalism
at one pole, versus openness, autonomy, and personal
freedom at the other pole. The second dimension— economic hierarchical
attitudes—relates to belief in hierarchy and inequality at
one pole versus egalitarianism, humanitarianism, and concern
with social welfare at the other pole. Right-wing authoritarianism
(RWA) and social dominance orientation (SDO) are the most
commonly used concepts that represent the first and second dimension,
respectively. Although these two right-wing dimensions
are often correlated, they are based on separate motivational schemas
and values (Duckitt & Sibley, 2009; Duriez & Van Hiel,
2002).
Many studies have focused on the psychological bases of right-wing
attitudes and prejudice. A recent meta-analysis demonstrated
that people with fewer cognitive resources are more likely to
adhere to social-cultural right-wing attitudes and tend to be more
prejudiced toward ethnic minority groups, whereas those higher in
cognitive abilities are more likely to endorse left-wing beliefs and
to be less prejudiced (Onraet et al., 2015). In one of the included
studies in this meta-analysis, intelligence measured at age 10
even predicted prejudice 20 years later (Deary, Batty, & Gale,
2008; see also Hodson & Busseri, 2012). Interestingly, cognitive
abilities primarily relate to the social-cultural dimension of
right-wing attitudes, whereas its relationship with economic hierarchical
right-wing attitudes is much weaker and even nonsignificant
(Choma, Hodson, Hoffarth, Charlesford, & Hafer,
2014; Onraet et al., 2015).
The full text of the meta-analysis of Onraet et al. is freely available on researchgate, so hopefully you can take it from there. Abstract:
The cognitive functioning of individuals with stronger endorsement of right-wing and prejudiced attitudes
has elicited much scholarly interest. Whereas many studies investigated cognitive styles, less attention has been
directed towards cognitive ability. Studies investigating the latter topic generally reveal lower cognitive ability to
be associated with stronger endorsement of right-wing ideological attitudes and greater prejudice. However, this relationship
has remained widely unrecognized in literature. The present meta-analyses revealed an average effect size
of r =-.20 [95% confidence interval (95% CI) [-0.23, -0.17]; based on 67 studies, N=84,017] for the relationship
between cognitive ability and right-wing ideological attitudes and an average effect size of r=-.19 (95% CI [-0.23,
-0.16]; based on 23 studies, N=27,011) for the relationship between cognitive ability and prejudice. Effect sizes did
not vary significantly across different cognitive abilities and sample characteristics. The effect strongly depended on
the measure used for ideological attitudes and prejudice, with the strongest effect sizes for authoritarianism and
ethnocentrism.
If I may comment, it's not a strong correlation, but it is there. They even include the relevant discussion in the paper:
For the statistical meta-analyses, we used the software
COMPREHENSIVE META-ANALYSIS version 2.2 (Borenstein
et al., 2005) in combination with metafor, a meta-analysis
package for R (Viechtbauer, 2010). We applied a random effects
model to compute the overall effects, because we
assumed that effect sizes would vary across studies.
Random-effects models produce results that can be generalized
to future studies with different designs (Hedges &
Vevea, 1998). First, Fisher-Z coefficients were calculated
based on the Pearson correlations to permit an unbiased comparison
of effect sizes. Second, we computed mean weighted
effect sizes and 95% CIs around the point estimate of the
combined estimates. Next, for interpretation convenience, the
effect size estimates were transformed back to correlations. According
to Cohen (1988), effect sizes (rs) of .10 are considered
small effects, .30 are considered moderate effects and .50 are
considered large effects. Based on an analysis of meta-analysis
in psychological research, Hemphill (2003) recommended
interpreting effect sizes of .10, .20 and .30 as small, moderate
and large effects, respectively, to better reflect effect sizes in
psychology per se.
And since someone mentioned this in comments, they also conducted an analysis of publication bias (see table 4 in paper and related discussion):
the PEESE results
can be regarded as the best estimates of the effect sizes corrected for publication bias (Carter & McCullough, 2014;
Stanley & Doucouliagos, 2014). Notably, these PEESE
estimates provide a somewhat less negative effect between
cognitive ability and right-wing ideological attitudes
(r =-.15) and between cognitive ability and authoritarianism
(r =-.23). All other PEESE estimates resemble the original
estimates.
If there is something that makes me doubt the universality of these findings, it is that most psychology studies tend to have a narrow range of respondents (the low-hanging fruit of undergraduate or graduate students). The Onraet et al. meta-analysis seems to escape that somewhat in that they seem to have a healthy dose of adults (defined also as 27+ y.o.) in the sample. It's not clear how far up in age the sample went, beyond that. The location was (predictably) mostly the "Western world", actually there's a heavy emphasis in the sample on US/Canada. Both of these issue can be noted in the moderator table (which is also probably interesting for other aspects, so I've included all of it below.)

And as sort of check further afield on the sanity of these findings... cognitive evaluations (IQ in particular) correlate fairly well with the level of formal education attained (that's one of the few things that critics and supporters of IQ testing don't disagree on). And since it's easier to inquire about formal education than it is to subject people to more detailed cognitive testing, it turns out there is a world-wide study by Hans Geser correlating formal education with the left-right political orientation, based on the widely used World Values Survey, which has a large sample (at least 1,200 respondents per each country included--note that in order to get representative aggregate multi-country results, the per-country samples need to weighted by the total population of each country.)
The results of this are somewhat more mixed and vary by country group (which is more or less geographical in this study, but they also use a linguistic/cultural grouping).

The more surprising finding here (to me) is that there was no clear pattern in the "Anglo Saxon" group, but there was one (in the direction confirming Onraet's meta-analysis) in Western Europe. Alas the Anglo Saxon group (Australia, Canada, New Zealand, Northern Ireland, United Kingdom, United States) was not further broken down in this paper, which would be interesting.
Less surprisingly, for the post-communist countries, which mostly buck the Western trend, it is observed/assumed that in these countries
the rightest leanings of educated strata may be explained by their particular abhorrence of former authoritarian regimes
Also, the World Values Survey has a broader focus in its political-orientation questions than the narrower ones many studies included in the Onraet meta-analysis, a lot of which focus on authoritarianism and prejudice.
Finally, I cannot offer much commentary on the Van Hiel (2019) study in itself. By its own abstract, it is the first to relate emotional intelligence to right-wing attitudes. For some numerical perspective/comparison, in the Onraet meta-analysis,
Fifty-seven studies showed negative relations, nine showed positive
relations and one showed a correlation of approximately 0.
So that is a good caveat about the validity of a single study (with a small sample).
Also, the Wikipedia article on emotional intelligence details some criticism of the construct, which some people have commented/hinted about under the question here; the validity of emotional intelligence as a construct/measure would probably make a good separate question...
Since some of the criticism against emotional intelligence is that it may lack incremental validity over IQ combined with "standard" personality testing such as the Big Five... I'll note that studies linking personality with right-wing attitudes are also aplenty, including a 2008 meta-analysis by Sibley and Duckitt:
The authors reviewed and meta-analyzed 71 studies (N = 22,068 participants) investigating relationships between Big Five dimensions of personality, RWA, SDO, and prejudice. RWA was predicted by low Openness to Experience but also Conscientiousness, whereas SDO was predicted by low Agreeableness and also weakly by low Openness to Experience.