I second Stocker for a racing game but Wonder Boy came out in 86 and I'd really like to see a game from the Golden Age. How about
Satan's Hollow - Arcade/Coin-Op. Dig Dug or Xevious would also be cool picks. RU has many versions of these two games. More options would be Gorf, Galaxian, DK, Robotron, Joust, Defender, Asteroids Deluxe, Time Pilot, Space Invaders, Galaga. So many cool games from that era to chose from.
Sports games are more difficult to come up with a good one for competition purposes but I'll try and come up with a suggestion.
For speed run, are you looking for something with an in game counter or just something that can be cleared and the ref will count frames?
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Here's a sports game that at least has a scoring system other than biggest blowout.
10 Yard Fight - Arcade/Coin-Op - Score Board. I've never played this game before but I have heard of it.