Somebody posted something just like this a few years back and I believe it was determined to be a piece of old Tile of some kind and maybe made of asbestos. Maybe someone else will remember it and chime in.
It's another head scratcher. The abraders I've seen online aren't as uniform as this one. There are lines are on both sides but they don't match up or anything. They are also different sized widths. However, the straightness of all the lines on both sides leads me to wonder if it is a piece of tile or something. Don't know about asbestos but they did/do make basalt grooved tile also.