Do they Mane Six really count as action girls? They rarely fight and they tend to do poorly against threats that aren't animals. When they fight things that are actually intelligent they either lose, it ends in a draw, or they use some kind of ass pull or deus ex machina to gain victory.

There are incredibly few instances of actual combat in the series. Let's break it down, shall we?

1. Vs Manny the Manticore, they performed admirably in the combat arts until they stopped due to Fluttershy's insistance.
2. While completely outclassed by a mad goddess, Twilight is able to trick her. All combat is deception.
3. Rainbow Dash kicked a dragon in the nose.
4. Twilight brainwashes a swarm of parasprites to fight the town on her behalf.
5. They don't comport themselves well against the Diamond Dogs, who admittedly are an unfamiliar foe with a home-field advantage.
6. Fluttershy suplexed a bear.
7. Twilight brainwashes the entire town to fight itself on her behalf.
8. Rainbow gets pinned under a boulder, has to get saved by a tortoise. Still, she did a good job of dodging the quarray eels that she was aggroing on purpose to showboat.
9. Pinkie Pie manages to successfully babysit for the eldritch abominations that are infants with instinctive magic use.
10. Fluttershy brainwashes herself to fight the town on her behalf.
11. The gang manage to fight a large army of shapeshifters, and do remarkably well despite literally overwhelming numbers. They did not go down to a mere 6 shapeshifters - it looked far more like they needed hundreds of mooks to go down.
12. Shining Armor throws his wife like a javelin.
13. Pinkie Pie brainwashes herself to fFUNt the town on her behalf. Twilight murders many pinkies for the crime of ADHD.
14. Twilight manages to trick another powerful tyrant into giving up its power through guile, rather than force.
15. Twilight remains an Enchantment-school afficionado as she decides to cast Hold Person at 7th level.
16. Power Ponies doesn't count, as the enchanted comic book would instill new instincts regardless.
17. Rarity brainwashes herself to beautify the town on her behalf.
18. Twilight has an out-and-out Dragon-ball Z fight with a superpowered magic-eater, and punches him through a mountain.
19. The gang manage to kick the flanks of a cult while being massively depowered.
20. The gang manage to send the Bugbear back to Tartarus without even being late for the wedding.
21. Twilight casts a spell that resembles Hold Person that is not attainable by mere mortals. By my count, she paralyzed 16 ponies as a concentration spell - if it were merely Hold Person, this would be a level 17 spell - spells of level 10 and above are the purview of Gods alone.
22. Twilight and Starlight have a feud that breaks multiple timelines. Starlight chose the terrain well - if Twilight goes all out, Starlight wins anyway.

After this point, my memory of the show gets a bit hazier.

I'd say yes. Fighting monsters still counts. As for intelligent foes, they're usually god tier level magical beings, so invoking deus ex machina artifacts is pretty called for. Changelings had a literal army, and they made a pretty good fight of it before being overwhelmed by sheer numbers.

Most of the large scale conflicts that aren't dealing with random monsters just aren't situations where an action kick to the face is a viable solution. I mean, yeah that would probably drop Cozy Glow real fast, but for her finale plot the Mane Six were basically sidelined completely because nobody knew who the actual villain was until it was too late.

They are action girls by the standards of action in the series, which is substandard compared to actual action series. It peaked with the one DBZ fight in Twilight's Kingdom, but DBZ has those all the time. And if they actually meaningly won the fights it would undercut the core message of friendship.

Action was never a priority for this series even if it was surprisingly good at first. It has inconsistent power levels, oft forgetting powers, and more often than not need a deus ex machina to bail them out.

I say they are legit Action Girls if their action was able to hold up as long/well as it did.