Basement partition wall sole plate - do I need sill plate gasket?
The primary function of the sill plate gasket is to keep undesirable stuff out, bugs, dust/dirt, outside air, etc., while at the same time keeping desirable stuff in, such as heated or cooled air.
While it can, and often is, used on interior walls in slab construction, it's generally optional there unless your local building codes require it.  You may want to check your local AHJ.