First of all any race can live an unnaturally long time with magic. Secondly Dunmer can live for a couple centuries even without magic and Altmer for several centuries without magic. Example: Divayth Fyr is a ludicrously powerful Dunmer necromancer and has lived somewhere around 1000(?) years as a result.
4000 actually.
And while it's true most elves die when they're around 100-150 that is mainly because of disease or violence, Nirn is a harsh world. It is however perfectly possible for an elf to live to be several centuries old if he lives a safe, clean, relatively disease free lifestyle, basically age correlates directly to quality of living, just as in real life. And as stated, some (all races) can live to be extremely old simply through magic, like the incredibly awesome Divayth Fyr.
I want to see that guy again, I refuse to believe anyone has managed to kill that guy yet, certified badass is what he is.