I'll start by pointing out a discussion about what actually is a game-rec. Which points out that the major things to look out for are actually not really to do with games; they're about being one of:
- A shopping recommendation
- An itemized list
What makes game recommendations so susceptible to this pattern is the fact that non-game-rec recommendation questions can be transformed into a problem. I'll repeat the example from there, the "gameplay recording question". You can ask it as "How can I record examples of my gameplay" because that's a concrete problem that you're experiencing.
Does it get multiple answers in that scenario? Yes, but that's no different than any other normal question that can get multiple answers. What makes it effective is that these are answers, not mere items on a list. And that the solution to the question, as a whole, is not the whole collection of answers, but can be found in a singular answer. It's what makes it different than one-per-answer, strange as it sounds.
So when it comes to a non-game recommendation question, check to see if it falls under the categories of being a shopping recommendation or an itemized list (or any other problem question, while you're at it). If it does, see if it can be transformed into anything better that can serve as a practical problem that you can face. If it cannot be transformed, then until it does get patched up, it is probably something that should be closed.
For your specific example question, one isolates the problem at hand - which appears to be "How can I track the games I play?", to be very abstracting. Make the question that, phrase it away from being "What sites are there that do X?". Then judge on the merits of that core question (whatever better interpretation of it you can make than that ill abstraction I made) whether it belongs or not.