That QR is enclosed cam. Enclosed cam QRs have the lever coming out one side as that does, not symmetrically. Another tip - avoid non-steel skewers like aluminum or titanium. Both stretch a lot more than steel and therefor have a lot less holding power. (The manufacturers of ti and aluminum skewers could make them just as good and still lighter if they did what they do on frame tubing - increase the diameter. Of course, that would mean needing bigger axles which would require frames with bigger dropout slots (and just what we always needed; a whole new bike standard!)

The reason not to use QRs for fix gear has nothing to do with the holding power. It is simply simpler to have nuts for an easy way to get the chain slack correct and center the tire between the chainstays at the same time with just two hands. Push wheel back to approximate correct slack. Tighten right nut. Center the tire. Like the slack? Tighten left nut and done. No? Barely tighten left nut, loosen right and correct the slack. Tighten. Repeat rear. Done. Takes less time to do than to write and not brain power or coordination at all. With a QR, you have to get slack correct and center the tire and close QR simultaneously. Fast, yes, but if you are having a bad day, maybe not even possible.

I abandoned QRs for fix gear hubs 45 years ago and never looked back.

Now, if you are using a bike with dropouts, not rear facing track ends, you can use the adjusting screws common on better frames to correctly set the chain slack and wheel center. Then, with one hand, you push the wheel back 'till it hits both screws, then close the QR. I use those screws on my commuter that I never change cog size on (but I still use nuts).

Edit: On good, cheap skewers - cheap Shimanos are really good. Not light, sexy ... but simply work. Less elegant and I wouldn't run them for as many decades, the cheap QBP steel skewers. Now, old skewers, including the very best, used an older cam design that didn't lock as securely. This includes the revered Campagnolos. That $10 QBP QR is a much more secure QR than the very best NOS early '80s Campy.