Unfortunately the hotel does not. However is equipped with a fitness center which includes steam showers. I will personally vouch for the steam showers, amazing for your skin :)
No pool. No hot tub. They have a couple individual steam sauna alcoves (kind of like a shower stall), but not very relaxing. I think they were getting ready to renovate the work out area so not sure they are still there
Get an answer from Executive Royal Hotel Calgary staff and past guests.