ROM Hacks make the process of developing a functional Sonic game with unique art, enemies, and modifications much easier, since the game engine and basic mechanics are already functional. However, if the game requires a different game engine, modifying existing low-level assembly may be inappropriate, and some game designers might choose to program their own unique game engine. The physics of a game engine are rules that describe how to transform the player's input (either in the form of buttons, keyboard, or even a mouse if the designer feels inclined) into appropriate changes in the position of the sprites in the game (such as the Sonic sprite, or alternatively, how enemy sprites will respond). These physics guides will hopefully make the process of simulating the rules used in Sonic games easier.
Since the rules themselves are independent of how they are implemented, many people choose programming languages such as Java, C, C++, Python, or a Lisp dialect to implement game physics. In addition, people can choose to use more specialized applications like Flash, Game Maker, or a Clickteam program like Multimedia Fusion 2.
Hopefully, these guides will provide adequate information to facilitate implementation.