The answer seems circular: because it works. The experience of people using Occam's razor (e.g. scientists) find MDL to be more likely to lead to correct answers than any other formulation.
I don't see that that makes other formulations "not Occam's razor", it just makes them less useful attempts at formalizing Occam's razor. If an alternative formalization was found to work better, it would not be MDL - would MDL cease to be "Occam's razor"? Or would the new, better formalization "not be Occam's razor"? Of the latter, by what metric, since the new one "works better"?
For the record, I certainly agree that "space complexity alone" is a poor metric. I just don't see that it should clearly be...
If you know more Eliezer Yudkowsky facts, post them in the comments.