[Vuejs]-Cannot read property `match` of undefined. I have no clues about it, since it doesn't point to any files

Your problem is the vue.config.js only exports the last object, each module.exports overrides previous exports.

The other problem you may have is that you disabled nodeIntegration, thus process will indeed be undefined unless you enable webpacks definition.

Edit:
To make require available on the renderer, you need to enable nodeIntegration in your background.ts file or disable it in vue.config.js.