Yet another situation where I try to understand the sentence hovering the mouse over one word and the dictionary hint just gives me the whole answer! Sure the sentence structure in this case isn't that obvious compared to English (meaning you can't exactly translate it word for word) but I'd preferred to have tried figuring it out by myself...
I answer "she made me room" and it's correct. I'm confused with this sentence and would have no idea to make one like that if the sentence really means "she made a room for me", because I tend to translate something literally most of the time. Can I go with "Sie machte einen Platz für mich".
"mir" can be shorthand for "to me," "for me," etc.
It's dangerous to only think about foreign languages in terms of your mother tongue (i.e. translating things literally) instead of accepting languages on its own terms. For instance, in Norwegian, when you want to say "unlock" (låse opp) you're literally saying "lock up," which, in English, means the opposite.
"Sie machte einen Platz für mich" may also be correct, but if you're only thinking in terms of English, you're missing out on the flexibility of the language.
It does not mean the same thing. When you "give someone space", you often walk away so that they have not just space, but have space all to themselves.
When you "make room for someone" or "make space for someone", you slide over a bit or remove stuff that was on the sofa so that there is space for them to sit down.
I agree, it's a very stupid construction. Meaningless actually, UNLESS (and after reading all the comments, I can see no one else has thought of this!) UNLESS you realize that maybe the speaker is in a competition, like a race, and "she" tripped or something, and because of that the speaker ended up taking 4th or 3rd place! She made me place! But that's pretty tenuous, I must say.