I think the
looking-for-game tag is excellent, but it's being used for two purposes right now. Some people are using it when they are looking for a game they remember details of but not the name of. It is also being used by people looking for games of a specific genre or setting, like "PS3 Games for Kids". I've seen the
identify-this-game tag and I think something like that should be used for the former purpose, and the
looking-for-game tag should be used for the latter option.
I think the
[identify-this-game] very clearly establishes the purpose of the question is to identify a certain game. So I think it is much better suited towards questions that are identifying a game of unknown detail.
[looking-for-game] I'm a bit hesitant, if only because it really can be different between "I'm looking for that game where you..." versus "I'm looking for a game where you...". One word difference for two separate meanings. The former is game identification (clearly covered by [identify-this-game]), while the latter is game recommendation. So since the focus is on recommendations, I would personally recommend [game-recommendations]. It's a bit stuffier than [looking-for-game], but it's very explicit in what it means and unambiguous. Possibly, actually, just shorten it to [recommendations], since it being about games can probably be implicit by this being a Gaming site.
On investigating for a retag, I noticed a [games-rec] tag is on a number of these. I think it would be wise to move these into a more concrete tag like [recommendations] or [game-recommendations], because [games-rec] is really not very intuitive. I think it's possible to confuse this for, say, "recording", which also uses "rec" as a shorthand. So I think it would be wise to move those over as well. The presence of that tag is making me lean towards the longer tag [game-recommendation], because the redundancy isn't all that bad.