So why not write that it's a spell? Why leave the DM to guess if it's supposed to be a spell or not, and if so what level?
There are at least two schools of thought on this:
1: "give them a full list of spells cuz it's realistic/useful for all situations, not just combat"
2: "give them in full detail what's relevant for combat, that's when I'm going to need their statblock otherwise they'll just use whatever spells I think they'd have. I don't want to have to flip around the spell section for it all, just print it on the statblock."
When we had the 2014 MM, you had folks like Matt Colville saying "I really don't need this huge list of spells that are never going to be used, 5e combat lasts for ~4 rounds and they're going to use their most powerful things; why do I need to know that they have sleep and charm person?"
And now that they've gone the other way, the vocal folk on the other side are speaking up. I will say that they SHOULD be stated whether or not they count as spells, or can be counterspelled, etc. I'm assuming that they don't state that based on folks comments here.
It just goes to show that you can't please all of the people all of the time!
a5e does something interesting though, which is BOTH. Their lich has a list of spells, and the combat spells' description are presented in the statblock, and also has (3e term) spell-like abilities like arc lightning and not-counterspell; afaik the latter can't be counterspelled.
Considering how concerned the a5e crew was about page space etc. in the AG, I'm surprised that they printed all those combat spell details in the entry... BUT it's appreciated.