What am I reading right now? You guys are confusing it with Life Weakness relic.
This relic does not deal damage, it periodically reduces enemy's max HP by 2% , hence why you see the dummy's HP bar going up (Max HP is reduced). You can see at the end, the dummy's HP became 30k (lost 40% total).
It can be good at the beginning of a boss fight, where you can reduce, let's say, the boss's HP from 100k to 60k in 20 seconds. Which could be faster than your damage, but if your damage is more than 2% of the boss's HP per second, then you won't really see its effect as you pointed out, so it's not really always useful in PvE.
In PvP, it is useful in prolonged fights, where the enemies either rely on HP for the power of some skills (e.g. Paladin) or against everyone really that keeps healing up to max HP time and time again, so you can get a better chance in killing them the next time.
Permanent skills will always reduce the amount prescribed even in battle.
Say you have 80, without a permanent skill, you would have 40 in battle. But now let's say you're using mermen gear. No battle would be 62, you would think that in battle you'd get 31 but in that case the mermen skill only consumed 9 points (40-31).
But what actually happens is that you would drop from 80 to 40 (in battle) then the mermen substract the mana regen, which makes you have 22 points, making it seem like battle is reducing more than 50%.
Gladiator's post in I don't understand how the terrible relic of sickness works was marked as the answer