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.
EVE is from 2003. DotA is too. Magic Online was from 2002. RTS goes well back into the 90s, simulators back to the 70s, etc etc. I'll give you Battle Royale and I don't even know what Rocket League is but most of these are not recent at all.
As the person said: the only new "type" of game they know of released the last years was Minecraft, and lists games from "early 3D" era, I assume the person is not aware of all the new genres of games created the last 20 years. The only goal with my post was to list some genres that might be unknown (some of which has been around for a long time). I hope someone reads the list and finds something new that they might like, you should try out Rocket League if you are remotely interested in games. Rocket League is an insanely hard (high skill cieling) physics based football-ish kind of game.
Simulators today are a totally different breed of games, no one that plays them now would consider them even close to what was possible to achieve 20 years ago, thats why I included them.
Edit: I meant to write Planetary Annihilation, not Total Annihilation in my original post. Which is a quite unique RTS.
Practically the same game, and the only ones in the genre.
Battle Cars was a racing game akin to Mario Kart i believe.
Probably there's a few more indie games that I am not aware of.
If you want to stick to mainstream games only, even then there is real innovation. E.g. calling Super Mario Odyssee a rehashing of Mario Galaxy does it a misservice (in my view).
You had completely new genres of games being invented almost every other year.
Today it is the same type of games, just re-hashing of the same content, maybe with more/better graphics.
The only most recent completely new type of game is Minecraft.... and walking simulators type of games. (although some one can say that they are just like old time RPGs).