For singleplayer I suppose it's something I never thought too much about? I just play what interests me and it's been more about my personal tastes. Long RPGs like Xenoblade or Persona are great singleplayer experiences but my introduction to Persona was playing the whole thing sitting next to my bf and it wouldn't have been the same playing it alone.
I guess my answer for a great singleplayer game would be a rhythm game? It's something you can keep coming back to and improve on and with some games having custom songs or beatmaps you can really personalize what songs you can play and sorta make your own music library, that's the reason I still have an interest in osu mania.
For multiplayer, I think accessibility is key, things like Mario Kart or Mario Party are easy to learn or teach people how to play so it's easier to play them more often or with more people. Stuff like Fortnite or Minecraft are easy because they're so popular, making them also accessible.
There are games that I'm personally engaged in, like I enjoy playing something like Monster Hunter Rise or Final Fantasy XIV or 100% Orange Juice with friends, but those are games that most of my friends aren't going to own. So it's more like I have a specific group chat with friends for if we ever want to play something like that.