I am not sure where you found that that Hittite sample was G-M406 as I couldn't find it in the supplementary data. But if it is, G-M406 is an Anatolian lineage peaking in central and northeastern Anatolia.
I have theorised that it spread with the Kura-Araxes culture to the Greek islands (and with the Greeks to southern Italy), as the Minoans almost certainly descended from a Kura-Araxes expansion.
If the other Hittite sample is J2a (I also couldn't find it), it would be from anywhere in the northern Middle East.
However the fact that these samples possessed Anatolian and Iranian farmers admixture with EHG and that they do not have any Y-DNA associated with Yamna or any other Bronze Age IE culture (R1a, R1b-L23, I2a2a-L701, E-V13, G2a-U1, G2a-Z1816, J2b2a-L283) is a good indication that these samples were in fact local Anatolian people assimilated by the Hittite invaders, and not Hittite themselves. Contrarily to what happened in Europe between 3000 and 1500 BCE, Indo-European migrations to Anatolia must have had a much more minor genetic impact, because Anatolian cultures had the time were more advanced and more densely populated than Europe (esp. Western and Northern Europe). The Hittites were merely a small ruling class, like the Goths in Italy and Spain. I doubt that they represented more than 5% of the population (or overall DNA in the gene pool after they mixed with locals) of their empire.
Additionally the Hittites arrived very late (1650 BCE) and were just an offshoot of other Anatolian IE speakers from Western Anatolian (Trojans, Luwians, Lydians, Lycians), who might have been in Anatolia for centuries, and before that in the Balkans, perhaps since c. 4000 BCE, giving them over two millennia to mix with Neolithic Anatolian/Balkanic populations. So it's hardly surprising if we find little Steppe DNA among the Hittites. In fact, there should be less of it than among Indo-Aryans in India (10-20%) because the Proto-Anatolians clearly left the Steppe much earlier (around 4000 BCE) than the Proto-Indo-Iranians (around 2000 BCE), yet the Hittites appear c. 1650 BCE, exactly at the same time as the Indo-Aryans in northern Pakistan and NW India!
What is going to be interesting is to see if the Anatolian IE tribes until the days of the Hittites also practised some sort of endogamy. I doubt it considering how all other Indo-European people freely mixed with conquered populations. We will know it once they find R1b-L23 (or other potential PIE) lineages among Hittite samples. If they have anything more than 5% of Steppe DNA, then endogamy might have been practised at least for a few centuries. If there is substantial Steppe DNA (say over 30%) then endogamy would have started very early after the Proto-Anatolians left the Steppe. But again, I very much doubt it.
The bottom line is that the two "Hittite" samples have non-IE Y-DNA and therefore can be expected to be assimilated indigenes.