Steam creates .desktop files for each game you installed, but it always sets the GenericName entry to "Steam Game". This purpose of this field is to allow programs with silly names eg "GIMP" to appear in menus as "Image Editor". This makes sense where the user just wants an image editor and does not know or care the actual name.

It doesn't make sense for Steam to do this, since while "Steam Game" is technically correct, a menu which just says "Steam Game" over and over does not allow the user to find the game they want.

Instead this field should be left blank, so that the full name of the game is always used. If you need to put "Steam Game" somewhere so that searches for "steam" will also find games, put it in the comment field.

This bug brought over from steam forums. A screenshot from XFCE showing the problem is attached, as requested. Note that the other games that don't say "Steam Game" were not purchased from Steam.