Material approach is correct. Export has a semantic meaning, namely something that goes out.
I don't recall seeing an export symbol with the arrow pointing down (or pointing inwards, for that matter), so I have no reference as to what other systems do and why. I do, however, recall examples where the arrow is pointing down, but those are for download, not export.
The Material icon version also corresponds with Gestalt studies on vector direction and, more loosely, with a newly proposed principle called Connectedness (not accepted by everyone because it's basically a combination of the existing Proximity and Continuity laws).
Additionally (and this is pure speculation on my part, so take it with a grain of salt), I think it also relates to their business model: Google products are cloud products, so the export concept should be about adding content to the cloud, not your own device.
EDIT TO ADDRESS COMMENT
The comment from user Big_Chair accurately mentions that they're using this for Import (which I missed in my initial answer, my bad).
This, again, is probably related to Google's conception of content has to be in the cloud. If you check the Material Icons List, you'll see the icon they're using is the File Upload icon (see below)
So this may not be consistent with other systems, but it is consistent with Google's philosophy: to import data to Google, you have to upload it to the cloud (please note that Material has no special icons for either export or import)