It appears that the app your talking about only played the audio from the video, stripping the actual video out and any ads that might have shown up. They also used YouTube in their name and where making money off the app. I'm not sure what Terms of Service I've violated, I'll have to take a closer look. Thanks for the heads up.
I think you're okay; I posted that a little hastily since it was linked to from the songza article that I posted elsewhere, but as you noted, your app doesn't have those same problems.
The one thing that I am confused about is why the old songza disappeared. If the only problem was that they weren't showing videos, they easily could have started doing so, and I remember that at least for awhile they were doing that.
Wikipedia says "However, in late January 2010 Songza had to put their music streaming service on hold due to problems with YouTube's API (which is what the site uses to play back songs), YouTube blocking the site from using its API, presumably because YouTube could be sued for supporting a free music service without adverts[citation needed]." It looks like Songza had ads, so maybe that was the issue. Regardless, you may find reading up about Songza interesting; TechCrunch reports they were acquired for high six figures to low seven figures.