I can't seem to reproduce this.. what happened after you clicked the button, did it go to the map screen and show the animation? Did the map screen have to load first? Did you see the result from the master bombardier?
After you logged back in, was the ICBM missing / city damage / indications that the battle actually happened?
Clicked missile test, selected 2 missiles, hit okay. Screen flashed and stayed there, no map screen and no result from bombardier. There was no damage to my city but I had a new vassal and I had expended my ICBMs
Do you know if you were completing the new chapter 3 plot point, to launch an ICBM? What screen did you open your player profile from? ie. Was your player profile open over the city, the map, news, etc..