I am wondering with what kind of languages such a multi-player online game was written?
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There are basically two types of web browser games from technological perspective:
1. Games that do not require server back-end (client only)
These are mostly casual arcade-like games - e.g. shooters, platformers and side-scrollers - which usually require no data persistence, networking or multiplayer capabilities, or which only require client side data persistence and multiplayer capabilities (e.g. hot-seat, split screen).
To create such a game you only require to create code, that will run on the client side.
2. Games that require server back-end (client + server)
These are more complex games such as turn-bases strategy games and RPGs, which usually require some server side data persistence, networking or multiplayer capabilities. It can also be simple client side games, that just require some ranking or top scores capablities.
These games also require the client side code, same as the games without the server back-end, but they also require the server side code, which will communicate with the client code to transfer and process the game data to provide the required persistence and multiplayer capabilities.
As for your question about what is sufficient, it mostly depends on if you require the server back-end or not.
For the server side, if there are no special and strict requirements on some of the aspects mentioned above, you could just stick with the programming languages and frameworks that you know and like to use, and it would be sufficient.