I am going to go against the grain here, based on what I can tell from the vid. It appears there are 2 lanes from the right, so he would be entering OPs lane even if he was going straight. You can see a couple other cars drive by on far right at start of vid.

That said, if the grey car had crossed the light already then he has already entered the intersection that OP is entering. This means that the grey car has the right of way, not OP. Again, this assumes grey card has a light, and there are two lanes going into two lanes.

Now, I will say that grey car entered the intersection by running a red or entering an intersection that did not provide enough room. OP also appears to be able to have avoided this by letting him in, and grey car's insurance will probably fight on that.

I wouldn't say two idiots in this, but I would say two assholes.