Since there are different Chess Federations and Draught Federations, I believe it would be best to leave both types of games on separate websites. I like the way Lichess has evolved into a dedicated, enlightening and user-friendly website.
The genuine chess game may have evolved over time, but the changes have been slow and within reason. Therefore, there must be a reason to have added the Three-Check variant on this site. I tried that variant and discovered that it is an enjoyable and education variant for the modern chess enthusiast. It permits us to practice a special tactic called: Pseudo sacrifice.
For the passionate variant enthusiasts, read up on the variant called: Cheskers.
http://en.wikipedia.org/wiki/Cheskers