Finish if you can, but get as far in the time and do as much as possible for each game mode if you can't. I know pretty much exactly what a game's going to get in terms of score way before the finish line, and also what I'm going to say about it. I half-write the review in my head as I'm going along, well before I put pen to paper. I usually start with some sort of anecdote or some kind of current event that I can link to the game in my mind, and figure out early how to begin the first paragraph and tie it together at the end. I then decide on the specific gameplay elements I want to discuss in detail.
I can't stand reviews that skirt over everything without really telling you anything. If I have a word limit, I'd much rather focus on the stuff I think is important, rather than waste words on overarching paragraphs of nothing.
Oh, and (possibly controversially, I don't know if everyone else does it) I do look at the Metacritic score and read a couple of other reviews for a game if they exist. "You copying bastard!" - actually, no, it helps me to make sure that my review's not retreading everyone else's ground. I try to be as little "me too" as possible in terms of the content, beyond the obvious stuff everyone has to talk about. Not the score, though - I don't give a gooseberry fool about whether it's identical or completely different to anyone else's, as long as I back up my points with a strong argument.
Most importantly, when the first draft of the review is finished,
that's the real starting point for writing the thing. Which is what many of the more mediocre videogame journos don't seem to realise. If they do, and their stuff is actually representative of much editing, God help them. I take far longer editing the thing than writing the first draft. I also like to write a draft early so that I can sit on it for a day or two. I then have loads of time both to edit in my head, and also to see it with fresh eyes the following day.
And yes, I've just gone into far more than the question asked. Whoops!