Almost all the chairs like that I've seen are some type of synthetic fabric. My bet is they are either olefin or polyester fiber or a mixed synthetic fibers so you can get fairly aggressive with them and really not be too picky about what cleaner you use. I have my own way of doing things though and I'm a stickler for using upholstery cleaners to clean upholstery. I have used some products that do a very good job on synthetic upholstery and carpet, but not safe for naturals. I'd also guess that those are pretty resistant to permanent stains, but will be attracting any kind of oily or greasy stain like a magnet due to the type of fabric on them. A citrus solvent usually does the trick on that or anything that will break up oily substances. You may not need anything other than just a good upholstery presray, brush it in real quick and hit it with your machine. It should only be a few minutes per chair. If I'm doing upholstery in the home I'm a lot more picky and choose on the spot how to approach it so I use at least a couple different methods. It can be a risky proposition to use carpet presprays on upholstery, especially until you really learn what you're doing. Best just to avoid that practice IMHO.
Btw, if there are a number of spots like that or if the chairs are fairly dirty I might choose to use a citrus booster along with my upholstery prespray if I think it will help the job.