In accordance with the documentation of Vuejs2, there are several keyboard modifiers, as you showed up on your @keyup.enter. In the case of the ESC button, there is the .esc, such as, for example, @keyup.esc or @keydown.esc.
So I don’t have to put this inside a input or button, may not be the best way, but I performed a demo below that will work whenever the ESC is pressed (or any key, as it is set to keyup, but there is a validation of the ESC key in the case keycode 27):
new Vue({
  el: '#app',
  created() {
    document.addEventListener('keyup', this.onEsc)
  },
  beforeDestroy() {
    document.removeEventListener('keyup', this.onEsc)
  },
  methods: {
    onEsc(e) {
      if (!e) e = window.event
      let keyCode = e.keyCode || e.which
      if (keyCode == '27') {
        console.log('Esc foi pressionado')
        console.log(e.target)
      }
    }
  }
})
<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.13/vue.min.js"></script>
<div id="app">
  <h1>Criar um evento que seja disparado ao apertar a tecla ESC</h1>
  <h2>Aperte a tecla ESC e verifique o console.</h2>
</div>