Mahjong Soul

Literally the point of the whole game, you compete with 3 (or 2) others and try to raise your score above other players.

There are ranks in the game where higher ranks lets you join higher rooms where you'll be able to compete with other players with similar ranking. This might be a balancing thing, but anything with ranks can be used as a bragging point.

You can't pause mid-game as you're playing with other players. To prevent you from taking long and inconveniencing others, you'll have 5 seconds and 20 seconds extra; this can be changed if you're playing in custom. Every turn you'll have 5 seconds to play your tile, failing that, it'll count down your extra which won't recover for that round.

Possibly if you have more cosmetics

The whole point of the game is to play mahjong with other people.

Limited time cosmetics

Cute anime girls

Cosmetics only

You get achievements mostly for just being good at playing mahjong and getting different hands, but there is an achievement section for the gacha part of the game

Doesn't really urge you to but there are small awards, or titles you can get for completing some of the categories