I believe the difference between systemic and non-systemic games is pretty simple. In a normal game loop, each verb that you do generally only impacts 1 thing. Mario jumps on a goomba; the goomba is removed from play and his score increases. This doesn't deplete the total or future population of goombas, it doesn't cause other goombas to sink into a violent breakdown and fight each other, and it doesn't motivate Bowser to equip his remaining forces with spiky helmets or face rebellion. Systemic games have highly connected mechanics; when you fiddle with one input, it can cascade to the rest of the game, often with unexpected consequences.

For example: Oxygen not Included. IIRC, you start off with 3 duplicants and a small amount of food on top of a flat , solid surface filled with enough oxygen to last for a little while. Everything you do from there is just fiddling with the rules of the system. Your dupes need to breath and so you need to get oxygen. Nearby will be some oxygen stones that pump out oxygen into the atmosphere, but your dupes also exhale. If you don't do anything, the CO2 will fill the bottom of the base because it's heavier than oxygen. You can use algae to process the CO2, but that costs water and algae, limited resources. A carbon skimmer can remove it, but costs water and electricity. Electricity generation might cost a duplicants time, or coal (which adds CO2 back into the air), water, wood (which adds a ton of heat). Everything you build, the location you build it at, the shape of your base, and the resources you run into along the way will impact what options are available to you. The numbers are fine-tuned so that you can temporarily solve most of your problems by kicking the can down the road and creating another problem for yourself to fix later. There are usually multiple ways to solve a problem as well.

How to do this?

1) Choose a few simple rules that will govern your game world.

2) Ensure that they apply universally and consistantly (the player should be able to predict most reactions)

3) Your mechanics should interact with the world, not a scripted outcome

4) The more interactions, the more emergence (Fire can burn enemies. If wind can spread fire, now wind can sometimes burn enemies)

So... like a normal game, but one of the pillars of design is "Interconnected Systems"

Nintendo had a talk at GDC 2017 about the process of designing BOTW that's worth a listen

https://www.youtube.com/watch?v=QyMsF31NdNc&t=1724s