There's very little lore for Genn, and while fun, a lot of the "Ask a Faction Leader" columns lean heavily towards satire and humor, less so towards being accurate to known lore.

Barring retcons, Genn should be in his 80s by the time of Cataclysm. Like most Gilnean men, he is a bulky, hairy guy. He was against the initial formation of the Alliance, was not entirely sincere when he agreed to join it, and ultimately abandonded it after the Second War. In the past, he has been manipulated by Deathwing and the House of Prestor. He did not get along well with Terenas and was disliked by Varian. He wanted to obtain the lands of Alterac. He wanted to kill the orcs rather than place them in internment camps.

After the Second War, he adopted a strict isolationist policy, leading to the creation of the Greymane Wall. During and after the Third War, his kingdom remained completely closed off from the outside world, and nobody was allowed to enter or leave. During this time, the worgen curse spread into the kingdom, and in time, lead to a civil war amongst the Gilneans.

He has a shirtless worgen son named Liam, but it's unknown if Genn himself is afflicted.

That's about all there is to know about the guy, so far.