close the door behind him 的字面意思确实是“关上他身后的门”，无论一个人通过门是“进来”还是“出去”，一旦他“进来”或“出去”后，门就在他身后了。所以将其翻译成“关上身后的门”也不算错，不过更多是将其翻译成“随手把门关上”“随手关上身后的门”。

这类用法有时还可以省略 behind 后面的 sb（此时 behind 为副词）。如：

He walked out of the room, slamming the door behind. 他走出房去，砰地一声把门关上。

Harry stepped into the passage and closed the door behind him.

网友可以把behind him(在他后面的)理解介词短语作后置定语修饰前面名词the door.   即the door behind him在那身后的那扇门。

behind在…身后（随手关上门）【英文解释: When you shut a door or gate behind you, you shut it after you have gone through it.】

I walked out and closed the door behind me.我走了出来，随手带上了门。

He slammed the gate shut behind him.  他砰的一声带上了大门。