Contrary to the spoiler, there is indeed a trait that gets around Resilient: Critical. Are there any non-psychic attacks with the critical trait? Psylock has critical, but the zombie is psychic immune. I'm sure I'm forgetting one. It's a rare ability, to be sure. I wonder if we'll get a war command incantation "head shot" that gives critical.
14 effective health is pretty good for 7 mana. Interesting that there's no point in giving it armor, not that there's a lot of ways you could.
Killing it with fire looks likely to take 3 rounds, maybe. A burn token is good for about 3 damage (less if you're in a hurry) and they need time to work. That's enough to let it attack at least twice, so it'll probably be able to trigger its own Bloodthirsty, which is pretty good damage from a 7 mana creature, too. Focusing attacks on it reduces the time to kill it, but does let it act as a tar pit. It's got pest, so it's not a good defender otherwise, so it may be hard in practice to get your opponent to try to kill it.
Sadly for the Warlock, ghoul Rot only works on living creature's. Interesting
I think Zombie Minion competitive value is going to depend a lot on the quality of the Necromancer's spawnpoints. Spending a full action to summon this guy seems like the biggest cost to playing the card. Lumbering means that positioning the Spawnpoint well will be critical, and it's going to be hard to defend with the Zombies, again, because they're pests.
Still, non-living and psychic immune dodges a lot of control effects. Whirling Spirit is pretty okay here, but Gorgon Archer or Basilisk isn't that helpful. A lot to think about here.