There was a solid green light (no arrows), and the only traffic coming from the opposite side was going to make a right turn. The cars at the solid green light just took a left turn anyways, disregarding the driver that's waiting to take a right turn; is that alright?
USA and other countries who drive on the right side of the roadway: The cars making a left turn were supposed to yield to the car making the right turn. General guideline (not a law or rule), if a car is crossing a lane of traffic, they must yield to any traffic approaching from that direction.
In countries where we drive on the right (USA, Canada, France, etc.), traffic turning left without an arrow must yield to traffic that has a green light; it is not alright for traffic turning left to go first.
In countries where we drive on the left (UK, Japan, etc.), things are different, and generally the reverse.
StephenWeinstein has it right and as you appear to be in Virginia, U.S.A. The left turning drivers were in violation of law. The traffic law clearly states that "all vehicles shall yield right of way when their path crosses the direction of travel of oncoming traffic." It doesn't matter if that "oncoming traffic" is turning right. It is still "oncoming traffic".
It depends what country you are in. If you are in the US turning right on a green light, you have priority over someone coming the other way turning left into the same road.
the left turn car did not have the right of way if they turned in front of the opposite traffic turning right.