If you need css that can't be applied by a style attribute like pseudo classes or media queries, what I do is the following:
Create a globally available style component when initializing Vue (you need it as otherwise you run into linting issues). It creates a style tag that simply renders the content in the slot:
I would only use this if you really need both dynamic values in your css and css features that can't be applied to a style attribute.
import Vue from 'vue'
import App from './App.vue'
import router from './router'
import store from './store'
Vue.config.productionTip = false
Vue.component('v-style', {
  render: function(createElement) {
    return createElement('style', this.$slots.default)
  }
})
new Vue({
  router,
  store,
  render: h => h(App)
}).$mount('#app')
Then use it at the top of your template like this and you get the full JavaScript scope of your component and the full css syntax combined:
<template>
  <v-style>
    @media screen and (max-width: 820px) {
      .gwi-text-media-{{ this.id }} {
        background-image: url({{ mobileThumb }});
      }
    }
  </v-style>
</template>
It seems a bit hacky to me, but it does it's job and I would rather go like this in some cases than having to add additional JS for mouse-over or resize events that have a big potential to slow down your application performance.