你好.absorb是个及物动词,后面必须加上一个宾语.
如果一定要用absorbing的话,句子就是：
Having absorbed himself in the computer games,the boy no longer put his heart into study.
或者：Absorbing himself in the computer games , the boy no longer put his heart into study.
我的两句中,第一句更符合英语的在非谓语动词形式上的习惯用法.