built a machine that can teach itself the rules of games of that sort and then：

and then 是and 连接了后面另外一个动词，别掺和进来。

and then, after two or three days of concentrated learning, beat every human and every other computer player there has ever been.—— beat 跟built 是两个并列的谓语动词。

built a machine that can teach itself the rules of games of that sort and then, after two or three days of concentrated learning, beat every human and every other computer player there has ever been.

built and beat...

【翻译】制造了一台自学这种游戏的规则的仪器，然后经过两三天的集中学习，打败了所有的人和其他电脑玩家。