"I was totally surprised by this, because it means that a (mostly) fully-functioning bot capable of playing arbitrary games of Magic: The Gathering has a small enough footprint to run locally on your machine"

I dont get that. Maybe I am missing something.

Lets say, the MTG AI was so intensive to run that it would be unreasonable to run on the customer's machine - then I wouldn't run it on the server either, since it would be quite expensive (and bot games in card games are usually not pay per play).

Also, servers are not magic - most of them run on the same x86 CPUs as the local machine, with a lower clockspeed than their desktop counter parts (but higher than (most) notebooks). Therefore, the only way to archive a lower Bot turn timer compared to running locally would be to use significantly more cores than the customer (usually 4-8, hence 8-16 allocated cores per player?!). Sounds like a nightmare, especially during peak concurrent player hours/days!

If the CPU Player does not support multi-core, running locally should be faster in any case.