In this sentence, "feels" refers to the impression or sensation the place gives to the person experiencing it. It doesn't necessarily mean they are physically feeling it with their hands but rather that the atmosphere or environment of the place creates a sense of spaciousness.
So, "It feels so spacious" means:
"It gives the impression of being very large, open, or roomy."
Your interpretation—"you feel that it is spacious"—is essentially correct!