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The Concord bed-chamber being always assigned to a passenger
by the mail, and passengers by the mail being always
heavily wrapped up from bead to foot, the room had the
odd interest for the establishment of the Royal George, that
although but one kind of man was seen to go into it, all
kinds and varieties of men came out of it.

that = used to introduce a clause of result (the chamber being always assigner to a passenger by the mail and the passengers being always heavily wrapped up from head to foot)?
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1. The Concord bed-chamber was always assigned to a passenger by the mail, and passengers by the mail were always heavily wrapped up from head to foot.

2. As a consequence, the room had an odd interest for the establishment of the Royal George.

3. This interest was that although but one kind of man was seen to go into it, all kinds and varieties of men came out of it.
Comments  
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Interest = Something, such as a quality, subject, or activity, that evokes this mental state?

Something = the strange fact = that although one kind of man was seen to go into it, all kinds and varieties of men came out of it?

Thank you.
Yup, that's about the size of it.

"interest" means a thing that the people in the establishment found interesting.

The thing they found interesting was that although but one kind of man was seen to go into the room, all kinds and varieties of men came out of it.
Ok, thank you.
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