No offense to the poster intended, but I can't imagine investing all that money in nice gear and not doing any room treatments. The easiest treatment is full carpeting. You can go with minimal carpeting or rugs, but to do so requires wall and ceiling treatments. Required reading:
Yup, beautiful rooms in their way, but your comparison to a gymnasium is relevant.
There are other ways to put absorption and diffusion into a room than covering the floor. The walls and ceiling are still wide open.
The first reflection points besides the floor are the walls near the front, the back wall, and the ceiling above the speakers.
Ok there is some carpeting on the floor, but look at all the fun they had with the ceiling and the walls!