I feel like a similar design could be implemented almost on any water way that is small enough, so I don't see how the drain configuration is a limitation. They probably don't want to put them where there might be wildlife, so they would only want to put them in rainwater runoff. This obviously isn't the answer to the entire plastic problem, but it seems to be helping.

What is specific about a circular drain opening for this to work?

I think the answer to this is the same as the answer to the classic interview question, “why are manhole covers round?” With a round hole, a ring of slightly larger diameter (to hold the net in this case) cannot pass through the hole, no matter what angle it gets turned. With any other hole shape (eg rectangular), the “ring” that sits outside the hole to hold the net can be turned such that it can go through the hole.