Well, the term "Old Rorikstead" as used in the song could just be for poetic effect, but now that you mention it, it doesn't really make sense that Rorik founded the town. Rorikstead is mentioned in Atlas of Dragons, which was written in the 2nd Era. I don't remember whether or not Rorikstead was also in Arena.
Well apparently the in-game dialogue does indicate that the Rorik you meet founded the town, I just looked it up to refresh my memory.
Rorik, a http://www.uesp.net/wiki/Skyrim:Nord http://www.uesp.net/wiki/Skyrim:Warrior_(class)#Warrior, is a former member of the http://www.uesp.net/wiki/Skyrim:Imperial_Legion and founder of the small farming community of http://www.uesp.net/wiki/Skyrim:Rorikstead.
When
if Rorikstead was named after him, he will tell the tale: "Yes, that's right. Look around you. Most of the lands you see are mine. Most of this I purchased while my comrades were fighting in the south, helping the Empire against the Aldmeri Dominion. Back then, nothing would grow here and so the land was worthless. Now, thanks to hard work and the gods' blessings, our farms prosper." He says he bought the land and founded the town after coming back from the great war, so obviously this Rorikstead is not the same Rorikstead as those that were around before, but I'm pretty sure it matches up to the one mentioned in the "Atlas" (with the dragon mound nearby). Unless there was an "old" Rorikstead there that got destroyed and he founded a new one, but it's a pretty big coincidence that the city he didn't found was named the same... Meh, I'm gonna go with this being an unfortunate oversight.