I'm going to try and chose games that I think are both popular/influential and I like. I.e. I'll leave out my favorite niche games and also popular games I either don't like or haven't played. With that in mind:
5. Mario Kart 8 Deluxe (1 point)
This title is important for 3 reasons. First, it's the best selling title on the Switch. Second, it uses motion controls which shows they haven't really gone away, and they are still popular. Third, the game is a port. Yeah the past decade is a decade of ports. So many ports. The most popular game on the PS4, GTA V, is a port. Porting has become hugely popular in the past decade and it's an easy way for studios to make a ton of profit. (So expect more ports....)
4. Minecraft (2 points)
This is the best selling game of the last decade. Also, it's pretty fun. More importantly it shows that a very large part of the gaming community really does not give a damn about graphics. Gameplay is what really matters. 2/3 of the console makers are putting all of this emphasis on graphics, but this game shows they actually have a major blind spot in doing so.
3. Undertale (3 points)
I like Minecraft, but I personally like Undertale a lot more. Great music, great story, great characters, and good gameplay too. This indie game checks a lot of the same boxes that Minecraft does. Graphics don't matter as much as the console makers try to make you think.
2. Breath of the Wild (4 points)
This game is great in so many ways. It's seen as innovate. Ironically, the innovation came from going back to the very first Zelda game. The freedom in BotW follows an old school philosophy, but it implements it in an entirely new way. That is real innovation. Remembering the best parts of the past, while extending out in a new direction.
1. Dark Souls (5 points)
It's the "Dark Souls" of innovative games. This game also follows an old school philosophy: tough but fair. At least the best old games were tough but fair (and the rest were just tough). Sony didn't want to publish the precursor, Demon's Souls, in Japan (or anywhere else), because they said the game looked bad. The reality is that the devs just focused on gameplay and level design until the end and then they prettied it up more. It shows. Put gameplay first and gamers will respond.