Coast Guard Approved or Not?
www.uscg.mil/hq/cg5/cg545/alerts/1015.pdf

I think these are illegal because you can't control the angle at which they can be seen.

This topic comes up about once a week. By definition, they are not USCG approved. The angle of visibility should be straight on to 112.5 degrees on each side. Anything else is up to your local GW/Lake Patrol. Many here argue up and down about it being OK, but the final say-so comes from the judge.
Just looking at the length of the strings and the shape of the bow, My vote goes for not legal, but then, who am I to say.
Stick with the factory installed lighting. Even some of those aren't legal, but at least if you get a ticket for lights, you have a defense in that you didn't install them.

I agree with Bob, most of what is out there is likely not meeting the criteria set forth in the USCG rules. I do believe that rub rail lighting could be made to be compliant, but would require a lot of testing and attention to detail during installation to achieve the proper viewing angles. I seriously doubt that is happening on most installations.

I will continue to runt he factory lighting on my rig for the reasons Bob stated, if mine is not legal then at least I can blame it on the manufacturer.

I do have lights installed under the rub rail, and have even been told by a GW that mine don't obstruct viewing the required nav lighting. But even given that, I rarely run them while underway. If you run into me while I'm anchored and using them to fish with, then you are blind and/or shouldn't be operating a boat in any conditions.