I recommend to add Tactics trainer for main games like chess,Draughts, and shogi. So it would be easier to learn that game. Or atleast chess puzzles ,( from lichess.org (or) chess.com )
Thanks.
I hope it would be useful!

Tell your ideas!

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Sounds like a pain to implement. Here are *open-source* puzzle trainer sites for games on PlayStrategy that I know of:

Chess
lichess.org/training
www.pychess.org/puzzle/chess (wtharvey puzzles)

King of the Hill
chessvariants.training/Puzzle/KingOfTheHill
www.pychess.org/puzzle/kingofthehill

Three-check
chessvariants.training/Puzzle/ThreeCheck
www.pychess.org/puzzle/3check

Antichess
chessvariants.training/Puzzle/Antichess

Atomic
chessvariants.training/Puzzle/Atomic
www.pychess.org/puzzle/atomic

Horde
chessvariants.training/Puzzle/Horde

Racing Kings
chessvariants.training/Puzzle/RacingKings
www.pychess.org/puzzle/racingkings

Crazyhouse
chessvariants.training/Puzzle/Crazyhouse
www.pychess.org/puzzle/crazyhouse

Variants Medley
chessvariants.training/Puzzle/Mixed

International Draughts
lidraughts.org/training/

Frisian Draughts
lidraughts.org/training/frisian/

Russian Draughts
lidraughts.org/training/russian

Shogi
lishogi.org/training
www.pychess.org/puzzle/shogi

Mini Shogi
www.pychess.org/puzzle/minishogi

Xiangqi
www.pychess.org/puzzle/xiangqi

Mini Xiangqi
www.pychess.org/puzzle/minixiangqi

Backgammon
opengammon.com/puzzle/ (registration required)

Honorable mention
OGS (no puzzle trainer)
go-problems (not open-source afaik)

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Go
senseis.xmp.net/?PagesForBeginners

2

on the topic of Go:

a puzzle trainer set (with even a grading exam system!) is on this new-ish app WeiqiHub
walruswq.com/WeiqiHub

2

About the game of Go you can find a lot

Many years ago I tried this:
http://gochild2009.appspot.com/

Now I also found this:
blacktoplay.com/

and an old side is this:
www.goproblems.com/

For more information look for the Go Association in your country:
for example something like this:
britgo.org/

3

Thanks for the suggestion @Hold_The_Trophy and thanks for all of the links @ll @woll @ronin3b

We do want to increase the learning tools for all our games on PlayStrategy and add Puzzles, however I can't give an estimated timeline for when these features will become available.

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