I don't think I'll spend the time to memorize the part for the anchor days, but the observation that March 0, 4/4, 6/6, 8/8, 10/10, 12/12 all land on the same day will definitely come in handy.
Silly mnemonics but it's something. The design about even number days all landing on March 0 / last day of Feb is a good and simple one. I don't know what Weekle is innovating -- instead of using an established system of mnemonics and calculations, he just presents his own table with no comments. Maybe his inspiration was to say, "hey guys, I made my own date calculation system" to impress people who don't know about Doomsday?
The goal of the web app is more about the practice modes and daily game, people are free to use Doomsday for these if they like.