This is actually a port to the real Amiga, and not one of those new exotic Amigas. But if you want to run AmigaOS 3, you can just use FS-UAE. In fact, that screenshot is from FS-UAE, as always copying things over to a real Amiga can be quite annoying during development :).

For AmigaOS proper, you'll need emulation. You can run AROS on just run of the mill x86 hardware, though, which is a pretty good alternative. It's source compatible with AmigaOS, and there's an Amiga emulator that lets you run 68k programs more-or-less transparently. It's a pretty good alternative.

I use the Amiga Forever package to run AmigaOS on my Windows 10 computer. Installation is quick and works flawlessly. I'm even able to remote in using Remote Desktop and access my AmigaOS from my laptop. There are 3 different versions with varying prices. (http://www.amigaforever.com/)

It uses the WinUAE emulator, which you can download for free. (http://www.winuae.net/) You would need to purchase roms to go with this though. The Amiga Forever distro includes roms.

Edit: Shameless plug: I used to run a CNet BBS back in the day and I got back into that scene by setting up another CNet bbs on my virtual Amiga. You can telnet to it at chksmak.cnetbbs.net:2600