New install of 10.11.6. Downloaded an app to install. Oh, gatekeeper, right. No "open anyway" button in the popup. OK, will change that in prefs I guess.

Went to prefs, was set to the middle option. Oh, there's Open Anyway there. Click. Installer tries to launch again, and same error pops up, can't open. Tried a few more times more in confusion that something so trivial could be broken, but it appears so. had to switch to open anything option.

I have had the same issue. The workaround is to Control-click the app and select Open from the contextual menu.

How much of your scenario might involve ( bad) code in the app?

Did this problem occur with any other apps?

I have had this occur with two apps.

How to Permanently Disable Gatekeeper in OS X El Capitan.

"It turns out that Apple quietly made a key change to the way that Gatekeeper works in El Capitan, and the feature will now re-enable itself (a.k.a. “auto rearm”) after 30 days."