The players there just seem to be playing extremely fast.

I know I can sometimes take even a couple of minutes to play a single move.

Maybe they are shown as playing fast in order to keep up with the anime's tempo?

The anime would be unwatchable if each game depicted took an hour or more. Obviously they are abbreviated.

Did you also notice none of the characters ever use the washroom? Do you think they are holding it for days upon days?

Ochi goes to the washroom, but only after he loses.