Hey Mach1, that is a diamond floor grinder and yes its what you will need. More than likely the rental place will have a similar machine made by EDCO that will work just as well but will be a little dusty if it doesn't have a vac hookup. Actually the blue garage was done with an edco, wasn't too bad with all the doors opened.
If you do rent one make sure they have diamond inserts and not the ones that look like cinder block.