Patch 5.0 Notes

[Wolflordval]

This is incorrect. Pets may no longer have health, but that doesn't change their status as entities. You can still move them, all their abilities are still used by them (and not by the summoner) and they can still act independently from the Summoner (i.e. they can attack one enemy while the Summoner is attacking another.)
I also remember someone from the Media Tour saying you can still click on/interact with your egi, similar to how you'd interact with Minions.

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."

[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.

[disturbedcobra]

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:

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.

They will be merged and the Egi Action I & II will change according to the corresponding pet. 3 of the 9 pet actions they formally had have been removed though.

Live Letter 51

[ArcaneCarbuncle]

They will be merged and the Egi Action I & II will change according to the corresponding pet. 3 of the 9 pet actions they formally had have been removed though.

Live Letter 51

Refer to my post, I literally explained how it (seems to) work, based off of both the Patchnotes as well as Media Tour Information.
These Slides are usually overly simplified and are often even slightly mistranslated; taking them as proof for anything if there is more reliable information out there is generally unwise.

[disturbedcobra]

Refer to my post, I literally explained how it (seems to) work, based off of both the Patchnotes as well as Media Tour Information.
These Slides are usually overly simplified and are often even slightly mistranslated; taking them as proof for anything if there is more reliable information out there is generally unwise.

https://youtu.be/3bPsBMzpKDE?t=36

They are pretty much like some other actions in the game. Like Bahamut's Akh Morn & Wyrmwave. They are there in the SMN action list but can't be triggered alone or placed in the hotbar alone. Instead you have to use Egi Assult to tigger them.

[ArcaneCarbuncle]

https://youtu.be/3bPsBMzpKDE?t=36

Again, the actions are still there, they are simply executed in the same way enkindles are.

EDIT:

They are pretty much like some other actions in the game. Like Bahamut's Akh Morn & Wyrmwave. They are there in the SMN action list but can't be triggered alone or placed in the hotbar alone. Instead you have to use Egi Assult to tigger them.

Yes, Egi Assault triggers the pet to use the corresponing skill; thats literally what I said?
The poster I was referring to implied pets weren't entities anymore and summoning them would simply change the Summoners own skills, which is incorrect.
Egis are still entities, and they still use their own skills, the method of commanding them to do so is the only thing thats changed.

[disturbedcobra]

Again, the actions are still there, they are simply executed in the same way enkindles are.

If you look I eddited my comment. Stated exactly that. XD