So while that is not an optimized mobile app, it is the browser version modified to fit a phone screen. It works mostly for newer phones but no guarantees. For more information read the following link.
It is possible to play Duelyst on your Android devices if you are connected to the same wifi as your pc with the installed steam client. You only need the free Steam Link App.
Unfortunately that means it doesn't work on Apple devices and not outside of your home wifi.
The Steam Link App practically streams the game to your Android device.
Video made by Jeremy Hooi.
Duelyst also works on an iPad Pro how Wimpish proves in this video:
Another setup is to use VNC to remotely take control of your PC (that has to be powered up) and launch Duelyst.
This runs very well in your home LAN for example to play on tablet or phone in every other room.
Using this method to play on 4G mobile network outside of your home wifi can be a hit and miss: It really depends on a consistently, persistently good bandwidth from your mobile operator AND from your home internet provider (upstream bandwidth).