Sabotage, border clashes and airstrikes happen all the time without constituting acts of war that give casus belli to their target. A basic legal condition of a just war is that it is proportionate and embarked upon as a last resort: launching a war because a dolphin you trained was killed is neither of those, as sad as it might be.
Sure, things happen all the time without a war breaking out. But it's not like you can "just kill" or "just attack" without repercussions. That's ridiculous thought. It's similar to saying "what's the reason to have a security guard in the shop, when you can just take a pistol and kill him". Security isn't about having an impenetrable defense; such a thing isn't possible. Anything can be destroyed in the end.
There's always a repercussion for attacking the military, be it diplomatic, economic or a military retaliation.
See, for example, the OED reference:
'An act by one nation intended to initiate or provoke a war with another nation; an act considered sufficient cause for war.'
https://www.oxfordreference.com/view/10.1093/oi/authority.20...
Granted, modern international relations has done a solid job of fuzzing the delineation of "acts of war" such that interpretations of acts can serve needs in a geopolitical context, but that will be the case whether you kill the dolphin or not.
These dolphins are protecting an area claimed by the military. Killing the dolphin would be an act of war. Even doing the same to non-live military equipment would be.
Obviously during wartime the dolphins would be vulnerable. But during peace time you'd think twice before attacking a military dolphin. You don't "just kill" them if you're not in war.