Nice examples of both machines. Gayety is indeed worth a bit more than Beach Club, in the condition.
If fully working and with a new piece of playfield glass (bingos use a slightly shorter glass than a typical flipper game), in your state, as much as $850.
Beach Club has a lot of great features for a static card game. Fully working and nicely cleaned up, in the condition shown, probably as much as $600-700ish.
$250 for each would be non-working/unknown condition.
These are definitely pinball machines. They have pins, balls, a spring-loaded plunger, playfields.... and on and on. They are just a different type of machine than most are used to seeing or working on. Finding a Gayety with a nice backglass is pretty difficult. That alone increases the value beyond $250 for me (if I were in the market), even if working condition can't be estimated. Fully working, by the way, would mean that the pockets and lines features work perfectly, the game pays in all positions, and game start, coin play, and extra balls are working, and all lamps function.
For Beach Club, it would mean that the game pays in all positions, and the special features like corners, super lines, and select-a-spot work properly, and all lamps function.