Back in the day, a lot of those games made a lot of assumptions about the hardware that it directly accessed. Even going from ARM 2 to ARM 3 to StrongARM caused a lot of problems for games.
The Archimedes had ARM 2 BTW, ARM 1 was just in the Tube co-processor for the BBC B. Some instructions are different with the RasPi, mainly to do with the PC register no longer having bits spare for Negative, Carry, etc. http://www.heyrick.co.uk/assembler/32bit.html has more details. There are external programs that detect and trap old 26-bit instructions when on 32-bit RO and allow old games to run but I know little about them; my last Acorn ARM machine was their R140 running RISC iX (a BSD port).