It does work with both circle and polygon the same way, make sure you are doing as instructed.
Select the tool and before doing anything type 8 and hit enter to confirm, then draw your circle or polygon and it will have 8 segments/sides.
Note: this method will set the default for that tool to 8, so each circle or polygon will have 8 segments until you change it or start a new instance of Sketchup.
The other option if you want to retain the default 24 or 6 and just draw one C/P with a different number, Select the tool and draw your shape, then type 8s and hit enter to confirm and the shape will change to 8 segments.





