HN is nominally an IT related site and "systems" usually means errr "systems" ie hardware or the things that run on the hardware. That could be games but that's just a special case.
Basically we are now at the point where a mathematician in a similar situation would dig out: empty set: {}, one: {{}}, two: {{},{}} ... ... yay - numbers, "now assume a spherical cow" and before you know it things get really weird.
IT isn't quite so clever but we do have some basic definitions and "systems" means: "systems" (####TODO: Fix recursive definition.) Systems can be designed and a Systems Designer might get involved in that activity. The more money that is paid to a vendor the bigger, better and more important the system - if Oracle is involved you will know this to be absolutely true. Games might be the focus of a system that is considered part of "systems."
A Games System Designer sounds like way too much fun to be involved in systems and so probably cannot exist.
Anyway, add Game to the title and we're all good. "Bestiary" is a nice touch but not quite good enough!
While it is definitely useful to have some of this background, and sometimes to get particular mathematical or physical simulation properties for a system you actually do need to pick these things carefully, in practice, to make gameplay configurable and tweakable it's often better to eschew the purity of mathematical functions and just use a configurable model instead. Unity for example has an object called an 'AnimationCurve' which can be used to make relationships between properties in a game highly configurable. Want to flatten the damage curve for a particular weapon to balance it out against a certain kind of armor? Don't struggle to adjust parameters for your logistic sigmoid to get it to behave, just add a point to the curve in the editor and drag it.
LUTs (look up tables) and other data driven designs are super useful in hand crafting a game experience. Especially if you want a discontinuous function.
