About the beggar relighting the Dragonfires with a torch:

I just assumed it needed a special kind of fire, so paying a beggar one gold coin to relight the Dragonfires with a torch isn't going to work.

Skyrim's Dovhkiin probably isn't born yet, so there's no way he/she could do this.

lol what a hot topic

My take on this is that the idea of Dragon-born is evolving here. Originally, the person in question had to have been blood related to Alssesia Slave-Queen (ASQ). Later the notion moved outward to include anyone who was a part of the ruling Cyrodiilic Empire who could claim to be Septim in some way. Now it appears that Dragonborn has widened again -- it seems to be anyone chosen by the Dragon God Akatosh. I don't think anyone could honestly say that all Septims were blood related to Alessia (in fact I'm not sure that Talos was) nor could we have any reason to make Dovahkhiin a Septim except by some sort of adoption. Dovahkhiin is a Nord concept anyway and may not be connected with the ideas behind Septimist Dragonborn ideology.

So I think the concept at this point would be annointed, not related by blood. And at least the way ASQ worded the compact no one not directly related to her born after the compact is covered. So unless Dovahkhiin is an Alessian Septim (and thus by NIrnian Genetics an Imperial and a noble) then he could no more light the dragonfires than he could sit on the throne.