Games for two means exactly that: two people on the same keyboard, or two phones passed back and forth. The rules are short, the rounds are short, and the result is known within a minute. Most of these titles are duels, so the skill is reading your opponent rather than memorizing a map.
Basketball Stars rewards timing and a decent release on the shot. Master Chess asks for patience and a plan three moves ahead, while Master Checkers is faster and punishing if you leave a piece hanging. Soccer Random throws the same idea at football, with a ball that behaves oddly and two players chasing it.
Start with Basketball Stars if you want noise and quick points. Pick Master Chess if you would rather think in silence.