Reading the list on Tom’s boardgame link to see how many I’d played down the years, I quickly found myself cheating: eg Dover Patrol is just a version of L’Attaque, so that counts as TWO etc. Then I started wondering, are there maybe a finite number of different game archetypes? : eg all bagatelles, shooting ranges, quoits are the same bagatelles, shooting ranges, quoits obv. but for example Peter Rabbit Race Game is really just a Ludo/Snakes’n’Ladders amalgam, with pix by B .Potter (ours had nice little painted metal figures too, the one pictured has lame cut-outs). Movie Maker, Chartbuster and Monopoly are all kissing cousins. Connect 4 is Naughts and Crosses plus one. Magic Robot is Trivial Pursuit’s primeval ancestor (the robot is not as magic as it looks on the lid, sadly). Taxi looks like a different take on a nice game we had when small called the London Game (where the board was the London Underground, and you had to visit Tourist Hotspots).
Is it just a race? Are you collecting sets of cards? Is money involved? Spatial strategy? Does it test a skill external to the board set-up (eg knowledge of trivia)? How elegantly reductively could you categorise?