In no way that is killing his career, it's the other way, it can make him more famous if it goes viral... DG made a drunk mistake but I don't see the "terrible" anywhere, just a broken individual opening up to another broken individual...
Terrible as in Alex was obviously gonna be pissed af, but DG was drunk and heartbroken so he couldn't give two shits. As for ruining his career, Alex's whole persona is about being a playboy who hooks up with anyone he wants. His viewers will lose interest if he gets a steady partner. Nobody will buy the a drunk friend was playing a prank on him. Drunk friends don't claim to be your lover. Maybe it will make him go viral as you said you never know. But i still stand by what i said. DG knew what he was getting himself into, Alex was very clear from the start. But it still sucks :/
I feel so bad for DG, he must be so heartbroken but i'm with Alex on this one. what he did was really terrible. You can't undone what happened now and that might kill his career as a broadcaster forever, people will always remember this and they'll stop watching his shows. They already started posting the stream fail. He could have done things differently since Alex was not leading him on and never promised him anything, from the beginning he was clear about what he wanted and DG knew what he was getting into and fully agreed to it.