This is our current badly-translated understanding of the rules presented in this video. If you spot any errors, please let us know.
This ruleset assumes that you have read riichi.md.
Galaxy Mahjong is played with a standard Riichi set. However, one copy of each tile is blue, and is known as a "galaxy joker". (The blue copy of the 5z is a 0z.)
Blue numbered tiles are rank-restricted jokers of that number; e.g. the blue 1m may be used as a 1m, 1p, or 1s only. Likewise, blue wind tiles may be used as any wind. Blue dragons may be used as any dragon.
If the dora indicator is a blue numbered tile, all numbers of the following rank are dora (e.g. a blue 7p being dora indicator means that all 8m, 8p, and 8s are dora). Similarly, if the dora indicator is a blue wind or dragon, all winds or dragons respectively are dora.
Having a hand comprising 14 galaxy jokers is a yakuman, called "Milky Way". This is valid even if the hand is open, even if it's won off a discarded galaxy joker, and even if the hand doesn't conform to the standard winning hand shapes.
If multiple players want to pon/kan the same tile, the next player in turn order has priority.
Concealed kans are displayed with all tiles face-up.
All other rules are identical to Riichi.
When playing with shuugi, each galaxy tile used in a natural meld/pair yields 1 shuugi upon win. (A natural meld/pair is one where all galaxy tiles are used as their non-blue equivalents.) e.g. a 7m blue-8m blue-9m receives 2 shuugi.