Not to get overly bogged down with definitions, but when you use the term 'DoT', the majority of MMO players are going to think specifically of debuff effects on the mob that apply interval damage to it at server ticks. Once you deliberately stray from this to the more literal and general sense of 'Damage Over Time', you won't have a meaningful discussion on the subject with anyone else. It just devolves into a semantic debate where people redefine the term to suit their convenience.

Living Shadow is time-gated and resource-gated. What it currently tests is whether you have remembered to save up 50 blood as you approach the 120 seconds mark. In that regard, it's a bit like Double Down. Although strictly not the same, it's also a similar kind of check to what the old Kaiten ability provided. These types of effects, while not difficult to manage, seem increasingly rare in what seems to be a trend to simplify gauge management on jobs down as much as possible.

You can make a case for Living Shadow having more interactive effects, perhaps tied to a finisher move next expansion. A standard damage up buff is probably the least interesting way of doing this. I personally want to see something that counts an effect used by the player (Edge or Bloodspiller) and uses that counter to determine the strength of an tag team finisher. You can also make the case for making it feel more responsive, with shorter summoning time. But I would rather see ways of improving and building off of the existing effect rather than replacing it with a standard two minute buff.