[Vuejs]-Form in VueJS is not checking if both inputs are empty

You could use Computed Properties and add value field to your inputFields. To check if the form can be sent, you can use every:

var app = new Vue({
    el: '#app',
    data: {
      inputFields: [
        {
          name: 'first_name',
          type: 'text',
          label: 'First Name',
          placeholder: 'First Name',
          required: true,
          validation_message: 'First name is required',
          value: null,
        },
        {
          name: 'email',
          label: 'Email',
          type: 'email',
          placeholder: 'Email',
          required: true,
          validation_message: 'Email is required',
          value: null,
        }
      ],
    },
    computed: {
      allowSubmitForm: function(){
            return this.inputFields.every(
              inputField => inputField.value != null 
              && inputField.value != undefined
              && inputField.value != '');
        }
    }
  })

<div id="app">
   <form>
      <input v-for="inputField in inputFields"
      :type="inputField.type"
      :placeholder="inputField.placeholder"
      :name="inputField.name"
      :id="inputField.name"
      v-model="inputField.value" />
      <button type="submit" :disabled="!allowSubmitForm">Submit</button>
   </form>
</div>