I'm with DFA on this; try it on an oil filter Lugz - (assuming it fits -if too small try a fuel filter or smaller size oil filter ? it could be for a specific use...) the strap is pinned on one side and the flat part will lever it tight.
Oil filter? On what, a 1914 Stutz Bearcat?

This thing is probably 100 years old. Look how ornate the handle is for a tool that is only meant to hold something for lifting or pulling without marring it. As for it levering, not sure I am following you. There is no flat part. It is pinned, it is a continuous loop, and that loop has a finite diameter of about 4".
It will fit on something round with that diameter or slightly less...
...but it would never be able to tighten itself around anything that needed pulling or lifting that is significantly less than 4".
And of course it would never be able to fit around anything of greater diameter that needed pulling or lifting.
But maybe we are just talking past each other.
To alleviate that, here are some of my strap wrenches.
The biggest one with the leather strap and the next one, which is canvas, are antiques. The red one is probably from the 50's. But note how they share a very similar shape, construction, and function, even though they are probably fifty years apart.
If you're not worried about marring whatever it is you're pulling or lifting, here is an OTC chain strap wrench.
Note that they are all adjustable.
Unlike the thing I found, they will work on smaller things...
or larger things...
...and they will cinch or snug it up.
These are what I am used to identifying as strap wrenches - in my experience. Maybe I am just ignorant on this. If you guys have something like the thing I have found an you use it as a strap wrench or you have seen something that looks like the thing I found and it was identified as a strap wrench, please point it out.