Actually, he didn't make that mistake - the pumps pictured are all pumping from east to west (the Z-level above is offset).
I'm not talking about designing a system that leaks diagonally from the pump output; I know he didn't do that.
He needs to feed power vertically into that bottom pump in order to keep the axles from being exposed to the magma coming up through the pump intake. He obviously isn't comfortable doing that, or he'd have just built a pump stack rather than an inefficient arrangement with a lot of axles and gears.
Alternate between these two z-levels, as shown before building the pumps or doors:
+.+. +: floor
+ .: channel
X X: stairs
.+.+
+
X+
Uses 10 power per level, for the screw pumps, and is completely sealed.
If you're really set on using that staircase arrangement, then do something like this:
Dig:
<++> upper levels
+++
+++..
<++ lowest level
+
+++. <-magma source
Build:
<++>
+++
+%%=* =: axle, *: gear
<++
# #: door
+%%.
Yes, this is magma-safe even though the magma seems to come "through" the axle.
Uses 16 power per level above the lowest (which uses 10), with one tile of axle and a gear assembly.
The OP's design, with a power staircase separate from the pump staircase, uses 27 power for each of the upper levels, and 22 for the lowest, due to the completely ridiculous number of gear assemblies. It's also designed so that magma can burn his axles and break his system.