These are the rectantular shields shown in one of the battle friezes, which appear identical to the 'classic' legionary scutum, but are apparently being used by the enemy troops, while the Romans themselves use large oval shields...
H. P. Laubscher (
Der Reliefschmuck des Galeriusbogens in Thessaloniki, 1975) believed these soldiers were Armenians, apparently because their equipment appears so unusual and distinctive, and the battle appears to be portrayed in a rocky landscape. The problem with this interpretation might be that the Armenians at the time were supposedly Roman allies, and fighting with Galerius to evict the Persian occupiers from their country!
Margaret S Pond Rothman, in 'The Thematic Organization of the Panel Reliefs on the Arch of Galerius' (
American Journal of Archaeology, Vol. 81, 4, 1977) instead supposes that the figures are indeed Persian infantry, and that the scene represents the final battle of the campaign.
It seems that nobody has any better theories than that! The campaign was fought in AD298, but the arch probably not constructed until c302. The men with the rectangular shields are certainly fighting
against the Romans, not for them - unless they're intended to represent a rival anti-Roman Armenian faction (still using old-style Roman equipment?), I think we'd have to assume they were Persians of some sort.