Yea Itch.io is a common publishing platform for games, not as prominet as Steam but it is up there, I have games on there too. Not all games are web playable, that is upto the developer in question. The site is commonly used to host game jams as it has a great set of tools for that purpose. Another platform I can think of is GameJolt, which functions similarly to itch but with more of a community focus than game jams.
I like to play Pokemon Tower Defense 2 from time to time, and depending on any stick figure games. I can't remember any other web games that I played as of recently.
Yeah it's on online. 3 probably still be a thing, but I don't know about 1 & 2 because they both work by flash, and flash will be gone on December 31st