The whole deal with red cards is that they're for gear that's mass produced, but they're produced for fairly narrow and specific theaters of war. They're things that you can find entire crates and wagons of, but the benefits they provide over mundane gear are fairly specific and/or situational.
For the Tree Killer, it's a fairly vanilla greatsword with a consistent low-level bonus and an inconsistent mid-level bonus.
The former — being able to use hooked weapons perform a modified shove that yoinks people around and deals damage — is something that I consider to be implicitly covered by the contested action rules, but it's not the sort of thing that everyone thinks of doing.
The latter — advantage against wood — is something that can be really useful in a really weird mixture of both combat and non-combat encounters. Need to stab a Treant? This is the sword for you. Need to saw through a support beam in a hurry? This sword will give you an edge. Need to fight off a demon? If they aren't made of wood, there're probably better weapons for that.
That said, I'm sure there's more than a few of you out there with players who will try to twist 'advantage against wood' into 'advantage against anything that contains wood.' So for the sake of clarity: this sword doesn't give you advantage just because someone is using a wooden shield.
Actual trees? Advantage. Living vines? Advantage. A plank in a perilous rope bridge? Advantage. Sawing a wizard's staff in half in the middle of combat or breaking someone's shield without having to perform a series of challenging contested rolls? Not a thing.
Jan 19th: Added +5ft reach to pull action.
May 18th: Template Update