The impression I got (based on very little information, so subject to change as time goes on) is that both organizations are taking the same philosophy that a job needs to get done and it doesn't matter that they aren't sanctioned (in other words, neither is sanctioned). Their claim seems to be that they'll do a better job because Coulson has been compromised by an alien serum that affects your brain function. On top of that, they think SHIELD needs more internal transparency among agents rather than being entirely need to know (and their decisions seem to be made by conference).
Of course, the original question is whether this is a coup. Keep in mind that SHIELD was stripped of its lawful authority by world governments, but it didn't necessarily relinquish it. Internally, the organization's leadership passed authority from Fury to Coulson. That authority isn't recognized by anyone besides SHIELD itself. Given that, it's possible to argue that no takeover would be a coup. On the other hand, it appears that Gonzales founded his SHIELD separately for the same reasons as Coulson around the same time. To the extent that any action could be a coup, it makes it less of a coup than if Melinda May had done the same thing.
It's also worth pointing out that, if Coulson has moral authority to lead SHIELD (since no one has legal authority) by virtue of Nick Fury passing the torch, it's not fair to hold that against Gonzales since he doesn't know that. He thinks Nick Fury died. Coulson has the toolbox, but they don't know how he got it.