What's the things you seek out in games? What kind of gameplay or story or visuals or cute gun grills will make you have more than a passing interest in a new release? I'll start off with a yuge wall of text that I didn't initially mean to write out.
It's gotta be fun solo. I can't stand games that are only really fun with a party stack. Having to wrangle four other people just to play the game without rolling the dice on randos defeats the purpose of a video game for me. Video games are better than other types of games because you DON'T need to get a group together and play, goddammit! I guess they're popular but I personally would rather just play a game that doesn't have bad solo experiences.
I love games with wide-open objectives/achievements that just drops you in and lets you decide how important they will be. One of my favourite things about Call of Duty games was building a class around some gimmick or weapon and then getting all the challenges available for it cleared. I spent a long time mastering every release weapon in Advanced Warfare because the challenge was there, and it seemed like something very few people had ever done. PS2 is no exception with its metric tonne of directives across three factions.
Games with lots of playstyles (and progression, though it's technically not really that much of a good thing compared to just unlocking everything from the start) are also super appealing to me. I loved TF2's nine classes, but you could even go further and divide the classes further with unlocks. PS2 has three factions with different weapons, ground, air, lots of classes with (somewhat) varied arsenals... I feel like I'm only halfway through it all and I have almost 2k hours in the game.
Games where the items/weapons feel good to use. The gravity hammer in Halo 3, the Gauss SAW in PS2, the Magnum in Halo 1, Home Run Bat in Smash, etc. It sounds minor but I'll play the FPS with good sounding guns every time over one with Mattel toys.
Games that don't remind you that you're in a game. 24/7 Hightower: no match ends, nothing breaking up your gameplay saying HEY we're gonna switch maps because this is a GAME and you probably could be doing something more important than playing a GAME. PS2 only breaks up a fight when the entire continent has been conquered, and the sky turns dark and death beams come from giant spaceships. A continent lock in PS2 feels like a good end to a session because they don't come up often. This is also a thing for singleplayer games, but definitely way more common in multiplayer games. It's not even really an "immersion" thing, just that I don't want my fun game to have to end and wait for the next round unless something really big happened.
There's some other stuff but this wall of text is big enough already. TL:DR I want a big game with lots of stuff to do, with stuff that feels appropriately powerful, and doesn't suck you out of the fun to look over stats and let the other nerds get doritos or something.
If you can't think of anything, maybe you have some red flags that will ensure that you don't pay much attention to a game?