Here is a list of new types of games that has come about the last couple of years that might be worth checking out if the only one you are aware if is Minecraft (this might sound snarky but I take you at face value and you might actually not have heard of these types of games before). Some of these have characteristics of old games, but often has stuff that was simply not possible 15+ years ago.

Sandboxed MMOS (EVE, no mans sky, Elite: Dangerous)

MOBA (Dota, HoTs, LoL, Smite)

Real MOBAs (WoW Arena, WC3: Warlock, Battlerite)

Battle royale games (Apex, PUBG, Fortnite, DayZ, ETF, Battlerite Royale)

Simulators (Arma, flight sims, truck driver simulator, which are now SUPER realistic)

Online Trading Card Games (Hearthstone, Magic [1])

Rocket League (I dont know any game like it nor what genre it is "sport"?)

Fast paced RTS (WarCraft, StarCraft, Total Anihilation, Red Alert)

Auto Chess (Autochess, Dota Underlords, Teamfight Tactics)

Competitive FPS (Call of Duty, Counter Strike, Rainbow Six Siege, Overwatch)

Casual social/arena action games (JackBoxTV, Use your words, Mario party, Overcooked, Duck Game, Gang Beasts, Speedrunners, Stick Fight, Hidden in plain sight [2])

If you are feeling old/and/or out of touch of modern gaming and coming from a perspective from the 90s, at least try these genres out. And of course games in the same genre has cross pollination and are similar in some ways, but some games play very differently, so don't dismiss a genre totally because you have tried only one game!

[1] One could argue that these are not a new type of game, but the mechanics in hearthstone is not possible in a physical TCG.

[2] Boardgame-ish types of games.

Edit: Of course I have left out a TON of games and some are actually considered quite old, these were the ones that came to mind.