I think you have things a little the wrong way around.
The tags are here to help people find puzzles, and there's only any point adding a tag once it has some puzzles to refer to. If you have (or can make) some good CTF-y puzzles, then make them and post them; if this turns out to be a genre of continuing interest, then we may need a tag or tags to describe puzzles in the genre.
One word of warning: your question uses the word "game" a couple of times; there's a difference between a puzzle and a game, and not all games are puzzles; puzzles are on topic here but games-that-aren't-really-puzzles aren't. The dividing line can be blurry, and different people take different views of exactly where it is. I don't know what sort of thing you have in mind and so can't really advise on whether it's likely that it'll be seen as insufficiently puzzly; the best thing is probably for you to make one and post it and see what the community makes of it.
Oh, one other word of warning: we do sometimes get things posted here that appear to be challenges from contests that are running elsewhere. It doesn't sound as if that's what you have in mind, but just to be clear: PSE doesn't accept questions from ongoing contests. (There's an exception for contests with no closing date, but usually CTFs don't go on for ever.)
So, in summary:
- I don't think we need new tags yet.
- If you want to post some puzzles of this sort, you should do so and see how they go down.
- If we end up having a substantial number of such puzzles here, then we may need some tags for them.