Updates: 4/21/20 - copy editing, note about layout change on OpenEMU's website, striking out emuparadise as its now defunct. The step process hasn't changed for iOS 13.
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The design on the OpenEMU website has slightly modified to make the experimental version easier to find Step 2: Install the MAME core This scfeenshot of the OpenEMU site is old. Go to and click the swatch and download OpenEmu Experimental, and install it. OpenEmu also sports MAME Arcade emulation support, but its a bit tucked away.
For users on macOS 11.x Big Sur and above (Apple Silicon and Intel) see the new updated guide: Mac MAME Arcade emulation & NeoGeo using OpenEMU and SDLMame for Apple Silicon or Intel. This guide is dated to the pre-Apple Silicon / Big Sur era.