They are simply emoting. As you know playing a musical instrument is a physical act and it’s natural to want to move with the music to one degree or another. I find that players in some European orchestras tend to “move” a little more than in American orchestras.
Now, and not meaning to get too “Zen” about this. Some pieces of music just seem to flow more at a particular tempo; arguably (but probably) the tempo, or very close to the tempo, that the composer intended. One of the many little mysteries in music performance. Obviously, some conductors sometimes have different ideas on tempo. I would say that Barenboim pretty much nailed the tempo sweet spot and he really got those Berliners grooving to Tchaik’s waltz. Having said all that, “”Waltz of the Flowers”! C’mon! Who can resist the lilt of a good waltz? https://youtu.be/f2_VsYfl2KU
That was a very young (pre-haircut) and very energized Gustavo Dudamel conducting for Pope Benedict (2006?) As I think you know, I prefer to not to talk too much about my personal professional experiences here, but this relates to Dudamel and the COVID situation discussed previously:
This past March I was in the middle of several days of recording sessions with the NY Philharmonic for an upcoming Steven Spielberg film of Bernstein’s “West Side Story” scheduled to be released in January of 2021 when all the COVID sh$t really started to hit the fan. The final sessions had to be cancelled and the project delayed (?). Dudamel was the conductor (with haircut). I must say that the guy is a huge talent to reckon with and very nice guy.https://www.youtube.com/playlist?list=PLCv8JuXLJXzqy788R77XZIFDLm8XkAVEz