I don't think the cartridge requires the use of a magnum length action but it is on the long end of the standard action capability.
Seems like any action set up for the 300 or 375H&H would be a close to ready to go although the H&H case has a rim .005" bigger so the bolt face would be a tad oversized.

Some cartridge overall lengths for comparison:
350 Magnum - 3.60"
400/350 - 3.60"
375 H&H - 3.60"
333 Jeff. - 3.48"
318 W.R. - 3.40"
The 416 Rigby is 3.72"