No, that portion of the sentence is not an absolute phrase. Absolute phrases will modify the entire preceding (or following) clause and can be dropped from the sentence with no impact on meaning. In this sentence: One thing was different however, each had the stoic look of money,
not the I’m better than you look, but the comfortable look of a wealth steward, the underlined portion modifies "the stoic look of money". We don't really know what that stoic look is until the underlined portion provides additional information.
The absolute phrase would look like this:
Standing with their arms folded, each had the stoic look of money. Here the underlined section is a modifier, but it modifies the entire clause, providing context for the overall situation and it could be easily dropped from the sentence.
Does that make sense?
KW