Option 1: use a computer for the website and a computer for MadMapper. Use the HDMI output of computer output and get it in the MM computer with a HDMI capture dongle (BlackMagic MiniRecorder is fine: https://www.ldlc.com/fr-be/fiche/PB00166107.html
Option 2: on macOS use Dekstop 2 Syphon
Option 3: do the same as option 1 but on the same computer: Screen 1 for the browser, HDMI out -> HDMI capture -> MadMapper -> Video Projector.
Option 4: use an iPad for the web browser and use WebNDI http://www.sienna-tv.com/ndi/webndi.html
So MadMapper could use the NDI stream (on macOS or Windows)
I couldn't find a Desktop to NDI solution ? I'd be surprised there is not.