Depends on your definition of “run”. Here’s someone that sideloaded the Xbox cloud app to run doom eternal on it (streamed from the cloud).

https://www.extremetech.com/gaming/316177-you-can-now-play-doom-eternal-on-a-samsung-fridge

On the other hand, these devices are most often just running Android. So you probably can install Doom on them. In case it’s not in the app store of the device, you could just grab an apk like this and sideload it

https://f-droid.org/de/packages/net.nullsum.freedoom/