Harley Quinn is the narrator (she had a thing for Capt. Marvel).
The comic starts 5 years before the first game. The comic shows that Billy is about 13-14 when Superman took over. So, he would probably be about 18-19 at the time of this panel (which happens in the game). Sure, it's possible that he was calling out to Shazam to turn into Capt. Marvel, but that's not how I read it at the time. I took it that he was trying to call down the lightning, but the other angle is interesting and I hadn't thought about that.
Edit: Watching the scene on youtube again, it would actually make sense that he was Billy dressed up in the hero costume. Even his voice sounded younger.