Presuming this is not suede......
Customers don't have a clue what to call this stuff. Microfibre is a pretty common term for it too.
HWE is fine almost without exception. Prespray lightly, agitate carefully because although in good condition they can take a hell of an agitation, some of these fabrics can show a kind of pilling effect, or the fibres can just strip off and leave you looking at the backing
Extract with much less pressure than normal - you're hardly cleaning any depth or volume of fabric at all so you need much less rinse water, otherwise you leave it soaking. Depending on the actual fabric, your machinery and your tool, you may find lock-down an issue, sometimes it needs a bit of a different technique with your hand tool to maintain airflow.
It's funny stuff when you wet it, and can dry a bit stiff but is fine after it's back in use and been vacced a couple of times. I'm more comfortable blow drying and setting the pile myself, I'd be reluctant to walk away from these wet.
One word of warning. If the wear areas look very dark, it may well be the backing showing through and not dirt. You really need a cheap little microscope to confirm this, and if so make it clear that you can't fix it.
I'd start carefully on a test area, dry it and set the pile before cracking on with the rest. Have fun
