I quickly learned the ominous undercurrents of Riften. On my first visit there, while stnading outside at the stables, I heard shouting in the street. I turned to see a running Imperial soldier get killed by a few Rift guards. Upon investigating the deceased, I found he was an Imperial Courier.

Since I'm (a newbie) in the Legion, was that courier trying to give me a message? And since he didn't, will I be missing some quest? Thanks.

Random event and has absolutely no relevance quest wise.

No. The couriers just run around all over the place. You don't get anything from talking/following them so you didn't miss out on anything.