Not sure, but I imagine the smaller and more integrated R8m used in the Alpha Chip uses smaller technology production (fewer nm) than the R8. That in turn might mean the Alpha Chip has lower power requirements.
I read somewhere the reason why the R8 was used in the final product instead of the smaller R8m is because the kickstarter rewards outnumbered the world supply of R8m chips. Don't know if that is true or not, though. It is also possible the R8m ended up being too expensive to meet the $9 goal.
None of this is based on concrete knowledge, so take it with a grain of salt.