Some kinds of stainless steel are non-magnetic. The advantage of having a non-magnetic ring is that your finger doesn't get pinched by strong magnets! This ring looks like stainless in the pictures. A jeweler could tell you for sure.
Also, the absence of markings does not mean a ring is not a precious metal-- most rings are mass-produced, and like any factory process, sometimes one will slip through without being properly stamped. Also, some home-spun jewelers and jewelry class students don't have a way to stamp their rings.