The one I have is semi-rigid and seems to be pretty similar to the last one tested in the video you shared which the guy says is fine.

It was done by the installers from the store I bought the dryer from when they installed the dryer at my previous house but beyond that I have no idea why they did that.

The rigid end is connected to the pipe by a clamp. I just attached more pictures to the OP that hopefully show this.

It seems like it's an oval duct to me but I may be wrong. How can I tell for certain?

Yes, you're correct, the duct in the first photo is a length of semi-rigid duct with a small piece of rigid duct and everything is round. The only thing that seems to be oval to me is the in-wall duct. What's the purpose of the rigid duct that has been attached to the semi-rigid duct?

What is the rigid end on the vent there for? Is that rigid end meant to attach to the dryer or the in-wall duct? If I'm understanding your comment with respect to the rigid end and the adapter it seems like the rigid end would normally attach to the in-wall duct.