In the Temple of Zhu Long, I had giant Sky-Scraper use her power to destroy an environment card, one of the Shinobi Assassins.
It’s a target, so she should do 3 projectile damage. Except, they can’t be destroyed. She did her non-target effect and did sonic damage to each target.
Is this intended?
The Assassin is never technically destroyed per its text so this seems like intended behavior.
I guess. But the text (seems to) key off of whether the card is a target.
“Destroy an environment card. If it was a target, Sky-Scraper deals 1 target 3 projectile damage. If not, Sky-Scraper deals each target 2 sonic damage and switches to her normal character card.”
This is the line from the card that is key
>
When this card would be destroyed, move it to the top of a Hero deck instead.
So it’s never destroyed per so being a target or not makes no difference. Therefore the second line takes affect for the Extremist variant.
Given this text, I agree that the first clause should trigger. The "If/If not" are strictly on "it was a target", not on if it was destroyed.
I think you could argue that neither would happen, as she didn’t actually destroy an environment card at all.
Thankfully, they ruled this (purposefully) that the alternate condition happens when nothing is destroyed. So, for example, if she triggers this ability and there are no environment cards in play of any kind (target or not), she still gets to do something. 
That is good!
Thankfully, also, it's a cooperative game, so other than in the video game, we are free to houserule whatever way makes it the most fun for us.