Could it be a compatibility issue with the Intel chip? I would think not, but this is unexplainable.
Correct. The CPU doesn't have anything to do with it. There have been other posts here though with people having trouble with fonts on the new Macs.
That said, there isn't (shouldn't be) any problem with fonts on an Intel based Mac. Are you keeping the Type 1 PS fonts together? That is, the suitcase of screen fonts and printer outline fonts in the same folder? It's required for those types of fonts in order for them to work.
And one other thing. If you try and copy them over while they are active (in a Fonts folder) on the other Mac, that won't work either. Make copies of them on the source Mac first to a dummy folder that is not inside any of the Fonts folder. The desktop will do. Then copy those duplicates over.