I am looking for a cheap 3d printer that can print this: https://www.thingiverse.com/thing:1307100 and is hopefully under US $200, such as the Creality Ender 3, Monoprice Select Mini Pro and V2, the Wanhao Duplicator i3 mini, the Anet A8, or the tronxy p802ma.
Pretty much any recent commercially available 3D printer should be able to print that model. Only really old stuff, or poorly built DIY machines, might have trouble. It may take some tuning of slicing settings to avoid problems with the rings bonding together during printing, but a more expensive printer is unlikely to make the tuning any easier.
The printers you listed in the question are probably all decent choices. I have an Ender 3 and like it but it's a little over \$200. There are some printers well under \$200, like the Monoprice Mini Delta, but I don't have any experience with them and product recommendations are off-topic here anyway. Also keep in mind that you'll have to spend a little bit on consumables, at least one spool of filament that's typically around \$20 (slightly cheaper for no-name brands, much higher for fancy color/shine/etc. or special materials, but simple PLA should be fine for what you want).