Some questions about games are allowed here. Broadly speaking, anything anime-style is allowed here, which means that games based on anime are allowed, as well as some other closely related types of games such as Visual Novels and some JRPGs. However, we do restrict the questions to be about the story rather than the gameplay of such games. Questions about gameplay of video games (as well as some story-related questions) are on topic on Arqade.
It's also not clear to me whether fanon games (like the one you posted) are on-topic. This isn't something we've really discussed up until now unless I'm missing something. Assuming I'm not, that's something we'll have to decide, and it's a tricky issue since we do allow questions about things like doujinshi which are also often fanon. My gut feeling is that this probably is off-topic here, but I can see arguments both ways. However, that's probably a topic for a different meta post.
There isn't a separate tag for video game related questions, and I'm not sure it makes sense to make one since we've removed the other medium-specific tags such as visual-novel and movie. You should use the series tag (in this case naruto) and specify in the question which game you're asking about. If the series tag doesn't exist yet, post it anyway with some other tag and make a note for what you think the correct tag is, and someone here will create it for you. Depending on the context, there may be other tags which are relevant (such as merchandise), but none that apply universally.