It does not qualify
The Extra Hex feat (and nearly all feats related to hexes) requires the Hex class feature, you don't have a Hex ability as class feature, you have a Hex as part of another class feature called Mystery Magic. For a class feature to count as another, the text has to make it clear that either it is not being replaced or that it works as that other class feature, as explained on this FAQ:
Archetype: If an archetype replaces a class ability with a more specific version of that ability (or one that works similarly to the replaced ability), does the archetype's ability count as the original ability for the purpose of rules that improve the original ability?
It depends on how the archetype's ability is worded. If the archetype ability says it works like the standard ability, it counts as that ability. If the archetype's ability requires you to make a specific choice for the standard ability, it counts as that ability. Otherwise, the archetype ability doesn't count as the standard ability. (It doesn't matter if the archetype's ability name is different than the standard class ability it is replacing; it is the description and game mechanics of the archetype ability that matter.)
Example: The dragoon (fighter) archetype (Ultimate Combat) has an ability called "spear training," which requires the dragoon to select "spears" as his weapon training group, and refers to his weapon training bonus (even though this bonus follows a slightly different progression than standard weapon training). Therefore, this ability counts as weapon training for abilities that improve weapon training, such as gloves of dueling (Advanced Player's Guide), which increase the wearer's weapon training bonus.
Example: The archer (fighter) archetype gets several abilities (such as "expert archer") which replace weapon training and do not otherwise refer to the weapon training ability. Therefore, this ability does not count as weapon training for abilities that improve weapon training (such as gloves of dueling). This is the case even for the "expert archer," ability which has a bonus that improves every 4 fighter levels, exactly like weapon training.
This is a similar issue with archetypes, like the Hexcrafter, that can take hexes from the witch's hex class feature, but do not gain that class feature. There are other archetypes, like the Unsworn Shaman, that grant you an alternate version of a basic class feature, but because the way they are written, they are no longer the same class feature anymore and can't qualify for feats.
However, Sean K. Reynolds (back when he was a developer) wrote a lengthy post about how things should work similarly, even if not explicitly written as such. In this case, even if the class feature is not exactly the Hex class feature, it grants you hexes and works like the Hex class feature, then it should be considered the Hex class feature for all purposes related to making the game run smoother and quicker. Do keep in mind, however, that this is not the rules as written for this, but a developer's opinion on the subject.
Personally, the ability is so similar to the Hex class feature (it even stacks with witch levels), that I would allow it to be considered a replacement for the Hex class feature in my games. Similarly to how I have allowed a Hexcrafter magus to take Extra Hex in the past for that same reason. This is one rules interaction that doesn't seem to affect game balance and is more restrictive and punitive to players than it should be, and could be fixed simply by adding the line:
"This counts as the hex class feature".
