While I mostly make posts about playing on OpenBSD, I also do play video games on Linux. There is a lot more choice, but it comes with the price that the choice comes from various sources with pros and cons.
Commercial stores §
There are a few websites where you can get games:
Itch.io is dedicated to indie games, you can find many games running on Linux, most games there are free. Most games could be considered "amateurish" but it's a nice pool from which some gems get out like Celeste, Among Us or Noita.
It is certainly the biggest commercial platform, it requires the steam desktop Client and an account to be useful. You can find many free-to-play video games, (including some open source games like OpenTTD or Wesnoth who are now available on Steam for free) but also paid games. Steam is working hard on their tool to make Windows games running on Linux (based on Wine + many improvements on the graphic stack). The library manager allows Linux games filtering if you want to search native games. Steam is really a big DRM platform, but it also works well.
GOG is a webstore selling video games (many old games from people's childhood but not only), they only require you to have an account. When you buy a game in their store, you have to download the installer, so you can keep/save it, without any DRM beyond the account registration on their website to buy games.
Your packager manager / flatpak §
There are many open source video games around, they may be available in your package manager, allowing a painless installation and maintenance.
Flatpak package manager also provides video games, some are recent and complex games that are not found in many package managers because of the huge work required.
Developer's website §
Sometimes, when you want to buy a game, you can buy it directly on the developer's website, it usually comes without any DRM and doesn't rely on a third party vendor. I know I did it for Rimworld, but some other developers offer this "service", it's quite rare though.
Epic game store §
They do not care about Linux.
Streaming services §
It's now possible to play remotely through "cloud computing", using a company's computer with a good graphic card. There are solutions like Nvidia with Geforce Now or Stadia from Google, both should work in a web browser like Chromium.
They require a very decent Internet access with at least 15 MB/s of download speed for a 1080p stream but will work almost anywhere.
How to manage games §
Let me describe a few programs that can be used to manage games libraries.
As said earlier, Steam has its own mandatory desktop client to buy/install/manage games.
Lutris is an ambitious open source project, it aims to be a game library manager allowing to mix any kind of game: emulation / Steam / GOG / Itch.io / Epic game Store (through Wine) / Native linux games etc...
Its website is a place where people can send recipes for installing some games that could be complicated, allowing to automate and distribute in the community ways to install some games. But it makes very easy to install games from GOG. There is a recent feature to handle the Epic game store, but it's currently not really enjoyable and the launcher itself running through wine draw for CPU like madness.
It has nice features such as activating a HUD for displaying FPS, automatically run "gamemode" (disabling screen effects, doing some optimization), easy offloading rendering to graphic card, set locale or switch to qwerty per game etc...
It's really a nice project that I follow closely, it's very useful as a Linux gamer.
Minigalaxy is a GUI to manage GOG games, installing them locally with one click, keeping them updated or installing DLC with one click too. It's really simplistic compared to Lutris, but it's made as a simple client to manage GOG games which is perfectly fine.
Minigalaxy can update games while Lutris can't, both can be used on the same installed video games. I find these two are complementary.
This tool is a set of script to help you install native Linux video games in your system, depending on their running method (open source engine, installer, emulator etc...).
It has never been so easy to play video games on Linux. Of course, you have to decide if you want to run closed sources programs or not. Even if some games are closed sources, some fans may have developed a compatible open source engine from scratch to play it again natively given you have access to the "assets" (sets of files required for the game which are not part of the engine, like textures, sounds, databases).