기차다 means "dumbfounded," "stunned," or "shocked," and, therefore, seems to have the same meaning as 기막히다, which I have heard many times before. Actually, when I first saw 기차다, the word 숨차다 (be out of breath) came to mind, and I thought the writer may have made a mistake by writing 기차다 instead of 기막히다. Of course, after looking up the word, I realized that I was the one who made the mistake.
By the way, I noticed that another definition for 기차다 is 정떨어지다, which means "become disgusted
From now on, I think I will finally be able to remember 기차다.