He was in the service of Torygg and helped an enemy. That makes him a traitor to Torygg.
He could've left Torygg's service and joined the Stormcloaks. That would have been honourable. Instead he betrayed the position of trust he held.

So did Torygg betray Torygg when he accepted Ulfric's challenge to duel?

It's hard to justify that because on one hand they are of the same people and country, so they share the same ideals and practices to an extent. But on the other hand they are of two different warring factions. So there's a lot of grey area, because they are kind of on the same side but not. Civil wars are tricky; in the American civil war there was brothers fighting each other on ether sides.

Roggvir knew Nord tradition, and was acting based on that. But the rules have changed, Ulfric is an enemy. And the Imperial army is in charge of solitude, and the Nords are not. If the Imperials weren't meddling with the Nords he probably wouldn't have been executed.

Yes, he was a traitor to the Imperials and their war.

No, he wasn't a traitor to the Nords and their way of life.

I never got why they killed him, he was hired to open the gate (which gate I don't know) when someone wanted to get through, now unless they were using that patented guard telepathy I hear so much about, how was roggvir supposed to know A: that ulfric had just killed the high king, or B: that the imperials had suddenly made an entirely legal nordic law illegal in the space of mere seconds of the act itself.

its like killing a man for eating sweetrolls the day before they make sweetrole eating illegal.

Don't forget even lollygagging is a crime in Skyrim.

Politics needs a scapegoat. Since they failed to execute Ulfric, they must execute someone else as a prove that they, the 'righteous' can correct the 'evil'.

I notice that some of the Stormcloaks have dialogue talking about saving Roggvir. Maybe you can legitimately save him if you don't enter the city until you invade it with the Stormcloaks. I'm glad someone could save him, though.