As of August 2021, there is only one online anime games that requires no download, completely playable through web browser. 

Mosha Online

[Video: https://www.youtube.com/watch?v=YkKEhcuReAo]

If you do not care online, then there is another one anime game that supports local multiplayer and also no download.

Touhou Diorama Duel

[video=youtube]https://www.youtube.com/w

Most of the free online anime games are of the MMORPG genre and free to download.
The following is a list of free online anime games to download as of August 2021.
Listed in the order of the most popular games on PC and console, according to the Best Anime Games Database.
Simply put, if the game is on top, it means you can play with more users. In online games, population is, in fact, one of the most important factors.

Free Online Anime Games

[b]Top #1. Genshin

A List of Anime Games for Android Free Download 2021 as of March 2021:
Genshin Impact

The Seven Deadly Sins: Grand Cross

DRAGON BALL Z DOKKAN BATTLE

AFK Arena

Summoners War

Honkai Impact 3rd

Fire Emblem Heroes

Epic Seven

DRAGON BALL LEGENDS

Fate/Grand Order

* This list is based on Google Play's Top Grossing list.