Vuex or not Vuex

I just starts learning Vue.js (awesome framework), and I get into Vuex. I don't understand the real use-case why I should prefere using it.

I mean I have a simple counter (like in the Vue doc):

Why should I use the Vuex syntax:

    const store = new Vuex.Store({
      state: {
        count: 0
      },
      mutations: {
        increment: state => state.count++,
        decrement: state => state.count--
      }
    })

    new Vue({
      el: '#app',
      computed: {
        count () {
            return store.state.count
        }
      },
      methods: {
        increment () {
          store.commit('increment')
        },
        decrement () {
            store.commit('decrement')
        }
      }
    })

While I can use:

 class Store  {
 constructor(){
  this.state = {
    count: 0
  }
  }
  /* mutations: { */
    increment = state => this.state.count++;
    decrement = state => this.state.count--;
  /* } */
}


let store = new Store();
new Vue({
  el: '#app',
  data: {
  state: store.state
  },
  computed: {
    count () {
    debugger
        return this.state.count
    }
  },
  methods: {
    increment () {
    debugger;
      store.increment()
    },
    decrement () {
        store.decrement()
    }
  }
})

Both works, and IMO the second one is much more simple??