I think it is just P2P in a sense that no additional third party is required, except for the connection establishment. It is still a client-server model. The difference is just that any browser can become a server hosting the game.

Even if P2P in this case meant that all clients were connected to each other, you could still have each client maintain its own state and only transmit the user input. I do not see why this should not work well as long as the majority uses honest clients.

Exactly, the real game runs on the host, the clients only send user input and Sync positions of the in-game objects, you can't use software like cheatengine clientside because it will always sync on what the host sees, but if you use it on the host all the changes will be shared with the clients connected.