Why are Bink compressed videos striped? If you've ever seen a Bink compressed color video, chances are it was striped and each second stripe was much brighter than the first. They went like this: bright-dim-bright-dim. Was it some kind of compression trick aimed at CRT displays that would blend the rows of pixels into evenly bright picture?

I don't have an example picture, but you can probably find an old PC game CD with a Bink-compressed video on it that has this striped pattern.
It sounds to me like you're describing interlaced video.  Which is, yes, "some kind of compression trick aimed at CRT displays," but has more to do with the perception of smooth motion, and less to do with brightness.  Basically, every other line comes from the next video frame, which may have the effect of making the lines brighter or darker.