Anything where the focus is the gameplay, and listening to characters in the game isn't some big part (or any part) of it makes for a good podcast game.
4X games like Alpha Centauri
X-COM
Defense Grid
RTS games in scrimmage mode
A Heroes of Might & Magic game
Beat 'em ups (Dragon's Crown and Capcom's D&D are good for this since they're longer than most others, also Guardian Heroes)
Fighting games
Puzzle games
If you like Darkest Dungeon
Really, just anything you can think of that you like that doesn't stop much for cutscene and people talking since you'll be listening to something else. Like, 13 Sentinels would be a bad game to play when trying to listen to something else, because you'll have to pause whatever all the time. Adventure games, RPG's that aren't combat focused, they'd be bad to go with.