There may be a possibility that the pump is a very flat centrifugal one on the electric motor's shaft, perhaps just below the bottom edge of the plastic drive pinion. That would make it very cheap, and although it would block far more easily than the usual positive displacement pumps that are used, it would not be damaged by the blockage the way most chainsaw pumps are. This could explain why they block so often on those saws. I've never heard of a centrifugal pump being used, but it would be interesting if that turns out to be the answer. Whatever kind of pump it is, it would be helpful to post pictures of it: I haven't seen a solution to this electric chainsaw oil pump problem anywhere on the internet.