No, it's an exaggeration.
In 2010, Russian males (aged 15+) consumed an average of 23.9 (Confidence interval 21.1–26.8) liters of pure alcohol annually. Including women brings it down to 15.1 (13.3–16.9) liters.(WHO; pg. 5)
(Note that the break-down is 37.6% Beer, 11.4% Wine, and 51.0% Spirits)(same pdf, pg. 13)
So, to be generous, even if we only look at the men and assume all the alcohol they consume is vodka.
Vodka is apparently usually about 40% alcohol by volume. So a liter of vodka would be 0.4 liters of alcohol.
Dividing 23.9 liters of alcohol per year by 40% by volume gives us the equivalent alcohol to 59.75 liters of vodka per year.
Dividing the annual consumption by 365 gets us 163.7 mL of vodka per day.
Even with a generous interpretation of the claim we are still pretty shy of 250mL.
Looking at these US tables (which only apply to US spirits measurements), the glass size falls between a "gill" glass (118 mL) and a "half pint" glass (200 mL) (which is strangely is not half of a (liquor) pint, or half of a US pint or half of an Imperial pint)]
A more accurate (but still generous) version of the claim is to consider all adults, not just men, and discard the 49% non-spirits drinks, but assume all the spirits S are vodka.
15.1 L per year both genders * 51% spirits / 40% by volume / 365 days = 0.050 L = 50 mL.
We are far too shy of the claim for it to be true.
the average Russian consumes about a pint of vodka a day; or, one-half of a half liter.
Note that "the average Russian" could be describing about the median value, not the average value. In which case, under perfectly ideal circumstances at most double our average, still being too low.