I suck at understanding the arts of war and battle. Has Muwatalli's reign brought new technology or tactics to the battlefield that was not present in the Hellenic lands at this time in OTL?
What is plain is that he has brought a high degree of unity; the peoples who have acknowledged his lordship are becoming numerous and his determination to take on dangerous actors like Phlegwas Crop-Burner has won him another legion of allies, who may not want to make him their king outright but would rather be fighting alongside him than against him. So he has been able to bring numbers to the battlefield, that much is clear. I can't judge whether they are fighting in a manner that would change the game of Hellenic warfare versus OTL, but a strong regional alliance and a large more or less federal power is a different thing.
There is a big innovation that Muwatalli has introduced and that he did not mean to- the rider on a horseman as a warrior in his own right, as opposed to simply being a mode of transportation. In this age such a thing rarely existed, and possibly hardly ever. This was primarily due to a number of things; horse breeding had not yet produced dedicated warhorses outside of those trained to pull chariots (and there were detailed and specific manuals on how to do so, see the Kikkuli text), and chariots were an enormously prestigious component of armies, to the point where it was assumed that any army worth its salt would have one. Across the past century many commentators have assumed that Mycenaean battles were primarily fought with charioteers. I personally find the artistic evidence of footsoldiers too numerous, and also question the likelihood of this when even the grand armies of the Mittani, Hittites, Egyptians etc had large foot soldier components even when there was over 1000 chariots in play.
So why is Muwatalli using horseback riders? It's a move born of poverty. Chariot-trained horses are a rarity in this era, as are the specialists who make chariots. They are incredibly expensive weapons of war, and thus Muwatalli entirely relies on his landbound allies to provide his charioteers. Meanwhile horseback riding is a fast way to move around the island of Euboea, and a fast way to move around the battlefield. But the saddles they are using are not very deep, and a lot of effort is spent making sure you don't fall off. The spear throwing and arrow-firing from horseback is thus generally forward facing, and tentative, to make sure you don't fall off the horse. It's why the arrows were so inaccurate when shot at specific targets, and why they didn't fight hand to hand- without sufficient support you'd just fall off. This is not the last time that the horsemen will appear in this battle, however.
As for everyone else, I'm glad that you enjoyed the two parts thus far, the third one should be making its appearance later today. I have to warn you, it's a longer one, but I think you'll understand why when it arrives...