That looks like black plastic from the furniture legs burned into the floor. that's horrible.
you're gonna have to get super aggressive to get those out. I think...
I'd wet chemical strip it with a dry strip pad. maybe a black pad too. maybe even a screen too.
yes, you'll need a 175 machine for sure or a square scrub machine. you'll also need something to slurp up the slurry with. I like a squeegee attachment connected to a porty. Also, you can fill the porty with nuertral cleaner for a killer rinse and use a lance to apply.
a mop bucket is handy too.
so, after stripping the heck out of it a coupe times and rinsing w/ nuertal cleaner and a nice damp mop finish.
now, you can start laying down your floor finish. I like a flat mop with applicator bucket.
I would put down a coat of sealer, then 3 or 4 coats of finish.
but those black stains look really bad.
is the floor damaged?
if the floor is heavly damaged it wouldn't hurt to put down an extra coat or two of sealer before applying finish.
have fun with that one!