Well, the date could be an issue as well – because I don’t think that the travel calendar plugin stores the occupancy dates in a single field, as a single value. If you think about it, one place can have multiple bookings, and that means multiple start and end dates. That must be stored in some sort of a structured data field, but it is defintiely won’t work with the date filter. Date filters are used to compare a picked date against a field, where a date is stored. But in this case, there can’t be a single date stored in the date field, if a room can be occupied multiple times. They probably use some sort of special custom coded structure and filter made exactly for their case for multiple booking dates.
The room capacity should still work, if that is actually a numeric field, if you try that with this configuration, and it works, then it is the right one.