When I purchase a game from itch.io, am I permitted to modify its source code? I’d like to integrate the game directly into my platform, enabling it to connect to my user base, retrieve user details, and send game outcome messages back to my platform. While we enable iFrames for embedding, we still need to communicate with the game’s code directly to report game outcomes to our platform. Are there any legal or technical restrictions I should be aware of when doing this?
In the vast majority of cases, no, but you should check the license.
Normally, when you buy a game, it's copyrighted. You can't re-upload or distribute the game, or modify the source code. Doing so violates copyright laws and is illegal; you could be hit with a C&D or DMCA.
Some people offer content under other types of licenses, such as the MIT license, and in those cases, you can redistribute the game. So you need to consider each case individually, and it's best to ask the game's creator directly before purchasing. Itch doesn't force you to use any type of license, so the license used depends on the original creator of the content and not the platform itself.
Would you have asked this question for a game you bought on Steam? Because the answer to your question is basically the same.
But since there is no real difference between a publisher/developer account and a user account on Itch, there is the asset section aimed at creators and there you will find things meant to be used in other projects. Those projects do include licenses or at least spell out what you can do or not do with the asset. Personal usage for games does not need a license, but using a thing in a project you want to distribute needs clear rules - mostly because it is not allowed per default. Not seeing a license does not mean anything goes!
The web games you see here are not assets. If you can buy them, you are not buying the web game. You are buying whatever download version of the game there is. If there are no downloads, a web game cannot be a paid game, it can only collect "donations".
