The poll doesn't try to make any claim about illegal votes or illegal registration. The voter profile does contain a page which says that 13% of registered voters in the poll were non-citizens (p68).
It does not state the status of these non-citizens, and it does not say where they were registered, or if they actually voted.
As the Washington Times notes, it may be assumed that these are visa holders, permanent residents, or possibly undocumented immigrants.
Permanent residents are allowed to vote in local and some state elections, so it makes sense for them to be registered.
The Washington Times Article
As noted, the poll makes no claim about illegal voter registration, and it is very well possible if not likely that all of those registered are registered legally.
According to the Washington Times, the 2 million claim comes from James Agresti who is the president of a right-wing think tank:
James Agresti, who directs the research nonprofit “Just Facts,” applied the 13 percent figure to 2013 U.S. Census numbers for non-citizen Hispanic adults. In 2013, the Census reported that 11.8 million non-citizen Hispanic adults lived here, which would amount to 1.5 million illegally registered Latinos.
Accounting for the margin of error based on the sample size of non-citizens, Mr. Agresti calculated that the number of illegally registered Hispanics could range from 1.0 million to 2.1 million.
As noted in this related question, extrapolating from such a small sample to such a large sample is error-prone and not generally done (even when starting with a correct small sample, which doesn't seem to be the case here). According to the calculations by Agresti, he extrapolates from 58 people who Agresti thinks are illegally registered (the actual amount of people who are non-citizens and registered to vote - maybe legally, maybe illegally, the poll doesn't say this - is 61).
Note also that even then, you only arrive at 2 million if you take the upper bound of the margin of error that Agresti assumes. It also seems that Agresti may have misread the poll or miscalculated. "13% of registered voters are non-citizen" (from the poll) does not mean that "13% of non-citizens are registered voters". (which seems to be what Agrestis calculations are based on)