Sims is a game which simulates moving through time. ‘Current year’ means ‘whatever year it is in the game’ or, more formally, ‘the game variable indicating the current year’.
In writing, of course, the YouTuber would have to do something to indicate that it IS a variable name, using things like capitalization, running the words together, different fonts, or quotes (‘CurrentYear’ e.g.) In speech, though, that information is conveyed simply by omitting the ‘the’.