Plus, in TWOK, the Romulan ale segment discussed it taking a while to ferment. Interpreting 2283 as a stardate provides a good long while for the ale to ferment; interpret 2283 as a year, and that part makes no sense.
Any year other than the current one would make the bottle suspiciously old for ale.
OTOH, if 2283 is to be interpreted as a stardate, we have to accept that 6000 SD units represent some fifteen years of Kirk's life - meaning the stardate system must have "hidden digits", or else stardate zero would have been within Kirk's original mission as well and most of the immediate Trek history would consist of negative stardates. Which doesn't seem to be the case, as we never hear of negative dates, but we do hear of old yet positively stardated events in TOS (such as the background on Kodos).
With hidden digits, Kirk would be left wondering whether the ale is fifteen years old, or a hundred and fifteen... And McCoy would be giving him a somewhat different reply!