Edit in JSFiddle

const home = {
    template: '<div>\
                    <div>[HOME]</div>\
                    <h2>ex.1 useage of v-model-link</h2>\
                    <div>chose: <input v-model="choseValue" v-model-link="\'/chose\'" @input="modelLinkCallback" /></div>\
                    <h2>ex.2 useage of $routerThen.push</h2>\
                    <div><input type="text" v-model="message"/>\
                    <button @click="routerThenClick">GO</button>\
                    <h2>ex.3 useage of $routerThen.modelLink</h2>\
                    chose: <input v-model="choseValue"/>\
             				<button @click="routerThenModelLink">GO</button>\
                    </div>\
             </div>\
                ',
    data() {
        return {
            message: 'hello, world.',
            choseValue: '?',
        }
    },
    methods: {
        routerThenClick: function() {
            this.$routerThen.push('/chose').then(vm => {
                vm.msg = this.message;
                vm.$once('input', value => {
                    this.choseValue = value;
                });
            });
        },
        modelLinkCallback: function(value) {
            console.log(value);
        },
        routerThenModelLink:function(){
            this.$routerThen.modelLink('/chose',value=>{
                        this.choseValue = value;
                    });
        }
    }
}

const chose = {
    template: '<div>\
                    <div @click="goBack">&lt; back</div>\
                    <button @click="chose(\'A\')">A</button>\
                    <button @click="chose(\'B\')">B</button>\
                    <button @click="chose(\'C\')">C</button>\
                    <button @click="chose(\'D\')">D</button>\
                    <div> {{msg}} </div>\
             </div>',
    data() {
        return {
            msg: '????, ?????.',
        }
    },
    mounted: function() {
        this.time = new Date().getTime()
    },
    methods: {
        goBack: function() {
            this.$router.go(-1);
        },
        chose: function(r) {
            this.$emit('input', r);
            this.$router.go(-1);
        },
    }
}

const router = new VueRouter({
    routes: [
        {path: '/',component: home},
        {path: '/chose',component: chose},
        {path: '*',component: home}, ]
})

new Vue({
    router,
    el: '#app',
})

$routerThen.initRouter(router);

<script src="https://npmcdn.com/vue/dist/vue.js"></script>
<script src="https://npmcdn.com/vue-router/dist/vue-router.js"></script>
<script src="https://unpkg.com/vue-router-then/dist/index.min.js"></script>

<div id="app">
  <keep-alive>
    <router-view></router-view>
  </keep-alive>
</div>