This timeline can't be right. Ulfric would have to be in his late 40s at the bare minimum.
He probably is, and the timeline is correct. The Great War ended with the signing of the WGC in 4E 175. The Markarth Incident was in 176.
http://www.uesp.net/wiki/Lore:Great_War#The_Great_War
The game begins in 4E 201, 26 years after the end of the Great War and 25 years since the Markarth Incident. How long Ulfric has been Jarl I can't be sure of, because I have yet to find documentation stating how long he spent in prison after he was arrested in Markarth. All we know is that his father died during his incarceration and Ulfric took his place when he was finally released and returned to Windhelm.
Prior to his service in the Great War, Ulfric spent almost ten years as a student of the Greybeards, starting at some unknown point in his childhood (he says he was "just a lad" but that's as definitive as it gets). We don't know when he left High Hrothgar to join in the fighting, but it had to be after the war started in 171 and before the sack of the Imperial City in 174 (since he was already a POW in Thalmor custody before that happened).
So somewhere in between 4E 161-164, he was already old enough to be chosen by the Greybeards and take up residence in High Hrothgar, and somewhere between 171-174 he was old enough to leave there and take up military service in the war. Personally I don't see the age of maturity in Skryim being less than 16, and I don't see the Greybeards taking in a child younger than 6 as student (not that this isn't possible, I just can't see them wanting to deal with a child 
that young, lol).
If you accept 16 as his youngest possible age in 171-174, then he's at 
least 43-46 when the game starts in 4E 201. I place him a little bit older by a year or two, but I think 50 is probably too old, if only because Galmar is officially described (in the game guide) as "old" in comparison and he seems 60ish, maybe 65 tops and there's a bit of a "paternal" vibe in their relationship (could just be me) which would seem out of place if they were closer in age.