Translation:That restaurant has already closed.
閉める and 閉まる are both about the closure of a spatial opening.
閉める means a closing action taken by the subject on the object.
I close the window.
閉まる means the state of the subject being closed or not. In English it is usually indicated by a present or past participle.
The doors are closing. (as we hear inside an elevator when the doors are about to be closed.)
The doors are closed.
Please note that there is still another word 閉じる which is also translated to close, and one more word 閉ざす which means to bar, to fasten.
閉じる is to "close" something to return it to its original, unused state.
I close the window (of a website).
I close my eyes.
閉ざす is about closing something as to block communication or access, especially mentally. e.g. 心を閉ざす. I also am not familiar with using it.
That would probably be もう閉まっていました ; this indicates a state of being that existed continously in the past, as opposed to もう閉まりました, which indicates an occurence in the past (of which effects are noticable in the present).
It's similar to 疲れました: "I have become tired" (i.e. "I am tired") vs 疲れていました: "I was tired" (literally "having become tired, I was").