All games can be boiled down to a one-phrase description. If you talk about real games, you can categorize them as "trick-taking" or "deck-building" and so on. The details are what make the games fun, not the basic mechanics.

(Therefore, "increment a number" games could theoretically be fun. Though I personally find them more boring than watching paint dry. At least the paint eventually dries and you can move on to something else.)