Okay, sometimes I'm slow. It took until breakfast this morning to figure out why Marines use a cutlass. I'm playing a Marine in atpollard's CT game. Naturally the character uses a cutlass. Why?
Maybe for a while Mssr. Miller was imagining Traveller to be a "laser pistol and cutlass" type game?
However, tradition is the most likely reason. I give three possible explanations for the origin of the tradition. Mind you, in the far future, where nobles wear ceremonial revolvers because they're "ancient" in the Imperium, swords would be too ancient to talk about, like marines carrying gilded rocks because that's even more ancient, I think a more recent explanation would be required.
Aslan. Perhaps during the Long Night, humans and Aslan dealt with matters of honor by duelling with swords (the Aslan were willing to permit it as it made duels honorable as humans lack a dewclaw). It fulfilled the honorable niche of fighting your foe face-to-face.
Battledress. Marines train with the cutlass when learning to use battledress. It not only builds strength and endurance, martial discipline and confidence, as most importantly, it teaches a marine to move in battledress without being a bull in a china shop, a very important skill.
If we assume that the majority of small arms encountered on a starship cannot penetrate battledress (and depending on the ruleset, this may or may not be true) then marines might carry cutlasses as functional weapons; if the enemy guns can't hurt you in your armor, bearing down on them with a cutlass (especially if it can cut through or damage spacesuits) is likely to make your opponents surrender.
Vilani. Perhaps they're called cutlasses, but the origin of the tradition actually lies with the Vilani, who are much more tradition-bound than those liberal Solomani and the weapon is actually Vilani in origin (the basic forms of melee weapons that are effective for a human to use are not great in number, so parallel evolution isn't out of the question).