Midway games are the carnival-style stalls that line a fair's midway alongside the rides: ring toss, balloon darts, milk-can toss, water-gun races, and similar tests of aim or luck. They're usually operated separately from the ride concessionaire and priced per play rather than covered by a ride wristband, with a small prize (often a stuffed animal) for winning.
See also: Fair Midway, the broader strip of rides, games, and food vendors these stalls sit within.