Spelling errors are highlighted using the SpellBad highlighting group. To get it highlighted as you want, you should put something like
hi clear SpellBad
hi SpellBad cterm=underline
" Set style for gVim
hi SpellBad gui=undercurl
after the last line that is altering the color scheme in your vimrc (it is either set background=(dark|light) or colorscheme {schemename}).
See also :h hl-SpellBad for names and descriptions of other Spell* highlight groups.