I doubt that information is readily available, but I'd guess both a lump sum
and some small part of the unit-by-unit profit as well, though Nintendo will
take the lion's share.  The AX machines probably have little to do with
Nintendo; SEGA has an established arcade business, but Nintendo hasn't for
years.

Amusement Vision should work on Monkey Ball 3 now!  Or maybe an original
title...or both.  Daytona came from a different SEGA team.  Let them do it.

if you know anything about nintendo and their history of controlling profit
margins per unit sold, you would assume that nintendo paid a fee to sega to
develop it, and that if sega is getting money from each unit sold, its a
very small ammount.

    The usual system (in North America, at least?) is that a developer
gets paid a lump sum to develop as an advance against royalties on the
first X units.  X depends at least on projected sales, developer vs
publisher clout, and estimated cost.  IIRC, I've read articles where many
developers never see sales high enough to substantially go over their 'X'.  
(This is an oversimplification in that the 'lump sum' is broken into
milestone payments payable every month to six weeks based on reaching
certain criteria.)