Okay so a few days back in Markarth on the roads, I encounter (seen them many times but never bothered with them) two rich looking people being escorted by an Imperial Soldier headed to the Vicci wedding. Now why they won't with all their money hire a carriage is beyond me, but whatever. For the first time I tell them "I'll be relieving you of those gifts" since I'm basically RPing a bandit/assassin, and the bodyguard fights me, I kill him, but they get away.

Well a while later (like a week in game I think) I'm walking along the road and encounter them again, and their bodyguard immediately draws his weapon without me doing anything and initiates the attack. I kill him and manage to kill the guy, but the woman gets away.

Do they belong to some type of special faction or something, because I ran into imperial soldiers between the two encounters and they never bothered me?

I have seen this as well. I believe that it is just another random encounter.

I could look up in the CK what faction they are part of...

Or I could look up on UESPwiki and hope to see an NPC-page where their faction is listed...

But I'm too lazy So I'll have to say that yes, they are probably in no faction and/or a unique faction, including the body guard. Or, the game might actually have some sense in the way of not every soldier everywhere knowing your identity after a crime... But I highly doubt that.