JSFiddle - React, Tailwind, and code Playground

JavaScript

class Title extends React.Component {
  constructor(props) {
    super(props);
    this.state = {
    data: React.PropTypes.shape({
    author: React.PropTypes.string.isRequired,
    title: React.PropTypes.string.isRequired,
    text: React.PropTypes.string.isRequired,
    like: React.PropTypes.number.isRequired,
    dislike: React.PropTypes.number.isRequired,
    likeState: true,
    dislikeState: true
    })
  };
  }

  this.LikeClick(index,el) {
  	//получаем index
    //если допустим у вас like - это массив 
    let likes = this.state.like
    let currentValue = likes[index]; //текущее значение лайка
    likes[index] = currentValue++ //увеличиваем значенеи лайка
    this.setState({like:likes}); 
  }


  render() {
    var data = this.props.data;
    var title = this.props.data.title,
        author = this.props.data.author,
        text = this.props.data.text,
        like = this.props.data.like,
        dislike = this.props.data.dislike;

    var newsTemplate = data.map(function(item, index) {
      return <div key = {index}>
        <div className="title_name"><p className = "title_textauthor">Title: {item.title}</p></div>
        <div className="title_text"><p>{item.text}</p></div>
        <div className="title_author"><p className = "title_textauthor">Author: {item.author}</p></div>
        <div className="title_rating">
        <p>Rating: <span className="likes"><i className="fa fa-thumbs-up" aria-hidden="true" onClick = {this.LikeClick.bind(this,index)}></i>{item.like}</span> //здесь передаём index
        <span className="dislikes"><i className="fa fa-thumbs-down" aria-hidden="true"></i>{item.dislike}</span></p></div>
      </div>;
    })

    return <div className="title">{newsTemplate}</div>;
  }
}