Rollercoaster Tycoon 2 only runs on PCs running Windows. PC in this sense means IBM PC compatible, that is backward compatible with the original IBM PC which used an Intel 8088 CPU. The 8088 was cheaper version of the 8086, and so this means all PCs use a version of the 8086 instruction set. Over the years Intel released CPUs that expanded this instruction set. Most notably the Intel 80386 added 32-bit support.
Being a 32-bit Windows game with a Pentium II CPU given as the minimum requirement, RCT2 would be written entirely or almost entirely using instructions supported by the 80386. The weren't that many instructions added by the later 80486, Pentium and Pentium II processors. A notable exception would be the MMX instructions, but these were hard to use and probably not useful for this sort of game. Also the original Railroad Tycoon supported Pentium CPUs, but only later "MMX" versions of the Pentium supported these instructions.
So the game works on Windows PCs that support a modern enough version of 8086 instruction set. This includes both Intel PCs and AMD PCs (and Via PCs), since all PCs have CPUs that use the 8086 instruction set. Any PC with an AMD CPU fast enough to run the game an acceptable speed would support a modern enough version of the 8086 instruction set. That would include all AMD PCs sold in the last 15 years.
Note that fact that a game was written in assembly language or not doesn't really make any difference to the end user. A game written completely in C++ will be compiled into machine code before being delivered to customers. Similarly a game a written entirely in assembly is assembled in to machine code. A Windows game, whether written in C++ or assembly, will only work on a Windows PC that supports a modern enough version of the 8086 instruction set.
The fact that RCT2 was written in assembly only makes a significant difference to the developers and publishers of the game. A game written in C++ can be ported relatively easily to other platforms. It's usually not as simple as recompiling the game to produce machine code for the other platform, but usually only a relatively small part of the C++ code needs to be changed. Porting RCT2 to the PlayStation 2 or PowerPC-based Apple Macs would require completely rewriting every line of source code.
There's project called OpenRTC2 project which has effectively done just that. They've reversed engineered the game and rewritten it from scratch in C. This has allowed them produce versions of their game that run on platforms other than Windows PCs.