Official name: browser, or more specifically: in-game browser.
Personally I don't know who would bother to visit a server's website, especially given that the regular MOTD is only there for a few measly seconds. The last thing I want to do in a game is use its browser too. Especially since, in Paintball's case, its resource usage is low enough that ALT-TABing out of the game is quick and painless.