I would like to know the legal aspects of embedding Itch.io games on my website; And disclose them in it.

If I understand what you're asking, this is really up to the individual game, not something that there's a general itch.io rule about. Most of the open-source/Creative Commons licenses allow rehosting and embedding under some reasonable conditions; if a game isn't licensed under one of those, then you'd likely need to get specific permission from the game's developer.