Patch 5.0 Notes

[ArcaneCarbuncle]

No, they don't. From the patch notes:
"Pet actions have been removed.
Actions that previously qualified as pet actions have been incorporated into player actions.
* Actions executed by pets have been moved to the Pet category of the Actions tab.
* Certain actions cannot be executed manually.
Pets can no longer be targeted by player or enemy actions.
* Attacks performed by a pet will generate enmity for the player who summoned it.
Pets will no longer be displayed in the party list.
Pet HP will no longer be displayed when targeted."

Yes, they do; you're reading to much into it.
I'll admit that the wording is misleading, but the pet skills are still there, we know as much from the Media Tour.
It also literally says they're still there, right below the part you bolded:

* Actions executed by pets have been moved to the Pet category of the Actions tab.

Wouldn't have to move them if they were gone.

All that change does is create actions similar to Enkindle where you press it to let your pet know which action to use.
Its there to clean up your UI so you can manage your pet's skills more effectively without having to set each to your hotbars seperately; especially important since we're now encouraged to swap them regularly.

Pet Healthbars being removed and their skills handled differently going forward are also largely unrelated btw; either change could have happened without the other, both changes just happen to be made at the same time.

As for pets still being targetable:

Pets can no longer be targeted by player or enemy actions.
Pet HP will no longer be displayed when targeted.

First line doesn't say pets become untargetable as a whole, it specifies player and enemy actions.
Second line also doesn't say they become untargetable, it merely states pet HP won't be displayed when they are targeted (due to Pet HP being gone).
The second one in particular implies they'll still be targetable.