Welcome to my Disappearing Act (Artful 💖 Pursuer) infodump (with pictures) -- I've loved this ship for a while now and making it as 'canon compliant' as possible has actually been really fun.
I think it's important to start off with the notable facts that make this weird stuff work -
Artful is (as of current canon) extremely mentally unstable. He killed an entire audience for making fun of him, and is traumatized mostly by his own actions, terrified of the same trigger that made him break. He doesn't believe he should be allowed to participate in society anymore, and wears his makeup constantly in order to ward anybody aware of his actions off. He sleeps in the woods to avoid people entirely and constructs his own shelters with his magic. At the most he'll venture into populated areas for food and supplies, but that's about it.
Pursuer is akin to a humanoid cryptid. It is intelligent enough to form vocal threats, teach itself to use tools proficiently, and hunt down prey relentlessly. While it has been referred to as 'put into a primal state', I see this as it is on a constant 'life or death' scenario as it's on the run from the government's containment. It is just a cryptid trying to live as free as it once was.
(Yes, Pursuer can talk. No, it is not 'just a dumb animal'. See the tldr for a good comparison.)
Now how do the two of them work?
In short, they are not a typical romantic relationship in any form. Pursuer is not interested in romance, and while Artful is, their relationship is based on not wanting to be alone during their most vulnerable moments, and finding someone who can fill the void, even if extremely unorthodox. It's not impossible for them to encounter each other in the wild.
Artful himself is inedible to Pursuer, due to the makeup at first, but he also has an advantage with his magic. Pursuer entirely relies on its own physical adaptations as a beast, and while it is built for killing, it can be rendered incapable by simple tricks Artful can do with magic, like levitating objects (possibly Pursuer itself) and creating constructs.
It's too much effort to make him prey, but it's less effort and even beneficial to the both of them if they stick together.
While Pursuer does not have romantic feelings for Artful (or in general), it accommodates what he needs out of a romantic partnership for "maintenance" to keep its part of the 'deal'. It isn't very social in any part of the sense, but will perform what it needs to in order to survive. And he trusts Artful's abilities to protect him if needed.
Artful in turn adores Pursuer's company, and while they still part when it has to hunt (and Artful greatly tries to avoid any gore) or when Artful goes to get supplies, he was always used to being around people, now around Pursuer. In reality he wouldn't be able to kill Pursuer, only defend himself if necessary, but he needs that security - he doesn't want to kill another person.
TLDR: Imagine crashing out and hitting rock bottom so hard that you go entirely offgrid and start dating Mothman because none of you want to encounter the government and face the consequences of your actions.
Thanks for coming to my Disappearing Act TED Talk.