Nope, that's Damage Health. Drain spells mean "For X amount of time, reduce (whatever) by Y points, and at the end of that amount of time restore it." Drain can be a very nice debuff when applied to certain attributes, and Drain Health can make very cheap one-hit-kill effects for things that have low HP in the first place - you can Drain Health Big Number Of Points For One Second, causing anything with Small To big Number Of Hit Points to die instantly but not really affecting anything with Even Bigger Number Of Hit Points at all unless they've already taken enough damage that your Drain spell gets rid of the rest.
So, re: Hair Shirt - in both cases, the shirt initially reduces your HP, then gradually restores it: note the duration of the Damage Health on the original shirt; it's only one second so you don't lose much HP, while on Alai's new version you lose slightly more HP (10 points instead of 2-6 points) BUT it comes back at the end of the 30 seconds. I think that's a fair balance for the increased magnitude of the Resist Magicka and Resist Shock components of the enchantment - bigger health decrease to balance the greater defensive properties - and even with the health coming back after 30 seconds, I don't think it's imbalanced since a: you don't get it back until your other defenses go away, and b: I always thought the Hair Shirt was completely awful compared to the items you can pay an enchanter to make for you; IMO these changes make it somewhat better and may give players a reason to actually use it. It IS an artifact, after all.