I can open the shapefile and its attribute table in ArcMap (10.8.1) as well. No issue at all.
I hope you are adding the shapefile to ArcMap via Add Data tool
or drag-n-drop from Catalog pane.
Do you receive any error message when you open the Attribute Table?
In case you are not able to see the attribute table dialog box at all (it should happen with other layers also), then please check Problem: ArcMap does not display the Attribute Table dialog box for a layer