How do I set initial state in Vuex 2?

I think you're doing everything right. Maybe you're just not creating the getters correctly (can't see any definition in your code). Or your setting the initial state not correctly (also not visible in your snippet).

I would use mapState to have the state properties available in components.

In the demo simply add users to the array in mapState method parameter and the users data will be available at the component. (I've just added the getter users to show how this is working. That's not needed if you're using mapState.)

Please have a look at the demo below or this fiddle.

const api =
  'https://jsonplaceholder.typicode.com/users'

const UPDATE_USERS = 'UPDATE_USERS'
const SET_LOADING = 'SET_LOADING'

const store = new Vuex.Store({
  state: {
    users: {},
    loading: false
  },
  mutations: {
    [UPDATE_USERS](state, users) {
      console.log('mutate users', users)
      state.users = users;
      console.log(state)
    }, [SET_LOADING](state, loading) {
      state.loading = loading;
    }
  },
  getters: {
    users(state) {
      return state.users
    }
  },
  actions: {
    getUsers({commit}) {
      commit(SET_LOADING, true);
      return fetchJsonp(api)
        .then((users) => users.json())
        .then((usersParsed) => {
          commit(UPDATE_USERS, usersParsed)
          commit(SET_LOADING, false)
        })
    }
  }
})

const mapState = Vuex.mapState;

const Users = {
  template: '<div><ul><li v-for="user in users">{{user.name}}</li></ul></div>',
  computed: mapState(['users'])
}

new Vue({
  el: '#app',
  store: store,
  computed: {
    ...mapState(['loading']),
      //...mapState(['users']),
      /*users () { // same as mapState
      	return this.$store.state.users;
      }*/
      users() { // also possible with mapGetters(['users'])
        return this.$store.getters.users
      }
  },
  created() {
    this.$store.dispatch('getUsers')
  },
  components: {
    Users
  }
})
<script src="https://cdnjs.cloudflare.com/ajax/libs/fetch-jsonp/1.0.5/fetch-jsonp.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.1.10/vue.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/vuex/2.1.1/vuex.min.js"></script>
<div id="app">
  <div v-if="loading">loading...</div>
  <users></users>
  <pre v-if="!loading">{{users}}</pre>
</div>