the most important factor is always the same: is it fun to play?
the second most important things i would say are stability (how buggy the game is) along with replayability (does the game get boring quick) and how much unique content the game has to offer.
while graphics are certainly a good thing to have, they do not necessarily make a game great. if a game already has the basics down pat they can sure make even more of an impact but they are not the most important thing.
the quality of multiplayer is also important in titles that make use of heavy multiplayer though a game does not necessarily need to be multiplayer to make it great.
the best reviews are always those which are from actual playthroughs. at minimum i'd suggest a reviewer play 25-50% of the game before making a judgement call. there are far too many reviews based on photos/videos/concept alone or very quick playthroughs with less than 3 hours of gametime. these help nobody.
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perhaps a few examples:
avp2 primal hunt vs the new avp game: the original has much worse graphics though in terms of fun factor and mechanics excels greatly. i personally consider it a better game than the remake despite the remake having better graphics. yes, the remake does have good points and i may be a bit jaded from playing it often but that is my opinion.
starcraft, total annihilation, command & conquer. despite being very low end graphic games there are still many people playing these classics today because they were made well and have high fun fun factor and replayability.
dragon age inquisition which is a fairly new release does a very good job. good fun factor, graphics, replayability. it fails (on ps3 version) on stability.
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then there are the games which mechanically would be great but are ruined by a pay-to-win type atmosphere.
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