Games to listen to podcasts while playing?

Binding of Isaac sounds like a game that would suit your needs

well you can always try games like Clicker Heroes

Card Crawl comes to mind first, and also the Reigns games (Reigns and Reigns: Her Majesty).
They're both relatively inexpensive, short game rounds and are turn based. Slay the Spire is good for that as well, but a little more costly.

I usually play turn-based games when I'm watching Twitch or a movie, etc.

Picross Touch (free), or Tales of the Orient: The Rising Sun. Need thinking but not full attention

City / Park builders (Cities: Skylines, Planet Coaster),
Horde mode (Killing Floor, CoD: Zombies),
Clicker games,
Rouge-Lites,
Management games (Factorio, Prison Architect, Project Highrise),
Exploration games (Subnautica, Slime Rancher, Stardew Valley).

diablo 3, torchlight - any arpg
city skylines - any "sim city"
minecraft
no man's sky
shadowrun

Minecraft (or such)
Marble Duel (or Luxor, or other Zumba-style games)
Idle or clicker games, for example: Forge of Gods
Match-3 like games, such as Bejeweled or Robo Match (enjoying this last one recently)
Other 'simple' puzzle games, like Lines (several versions)

I chose games that have minimal text, and that can be muted without losing valuable content.

Rogue Legacy, if you like action platformers
FEZ, to get your mental gears grinding
The Witness, if you want to twist your mind even more
TrackMania, to race with grace

I listen to podcasts while playing FTL (maybe that's the reason I'm so bad at it).

Casual, sims, deck building

Borderlands 2 if you've already done the main story or if you're just getting some xp.
Starbound <3
Ultimate Viscera Cleanup Detail

I sometimes listen to podcast or documentaries while playing arpgs like Diablo 3, Grim Dawn or Path of Exile.

On a slightly different note... I would really recommend listening to podcasts while exercising! Forgive me, I know this is a little off-topic, but when I've read " its just feels so much productive to be doing 2 things at once!" I immediately thought about me catching up on some YouTube series on a treadmill! I had a lot of work lately and unwatched videos kinda stockpilled themselves, so I thought about watching them on my tablet instead of listening to music while running... and it worked out great! The time passes so quickly and it is easier to forget the pain and/or the fatigue.

Going back to games though...

I've never listened to podcasts while playing, sometimes I put on some streams as a background noise, but that doesn't get much of my attention.

BUT, I think that Dungeons Defenders would work out (it is a TPP tower-defence, with simple but fun character developement; you get a short planning phase, and then a lot of mindless enemy smashing, so it does not require a lot of concentrating, but is very rewarding). Also, I think Minecraft, Terraria and Stardew Valley are addicting, but not really attention-absorbing. Additionaly, some online shooters (or shooters without an engaging storyline) and racing games should be nice, but I don't play much of those.

Creeper World 3: Arc Eternal

Meatgrinder tower offense that makes you work hard for every inch of ground on most levels. It can be played more rapidly, but the slow and steady approach would be perfect for podcast listening. Enough strategy and reward to be interesting, but you can let your brain focus elsewhere. And it's just a great game.