That certainly seems to be a tenor, too large for a C-melody—which is just a 'c' tenor anyway.
Lots of bands posed with huge racks of instruments by whatever maker they were promoting. But Polo seems to have the tenor, his clarinet, a soprano..and perhaps an A clarinet as well? Most clarinetists used to carry one for sharp keys, especially Albert system players.
Essentially all Bflat horns, so I suspect he's getting use from all of them.