The vim-path variable contains the name of the vim executable. The default vim-path is "vim". Which is not very useful, as it starts vim in the same terminal where you started factor.
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If you want to use gvim instead or are on a Windows platform use editors.gvim.
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If you want to start vim in an extra terminal, use something like this:
{ "urxvt" "-e" "vim" } vim-path set-global
Replace urxvt by your terminal of choice.
You may also wish to install Vim support files to enable syntax highlighting and other features. These are in the resource-path in misc/vim.