Riichi is the most fun one, in my opinion, but I would not go so far as to say "skill weights over luck". The absolute best Riichi players win less than 25% of hands.
Riichi is a good candidate for a video game due to all the specific rules. It has a lot of room for QoL. I have an app on my phone [1] that has made it fun to play and learn thanks to the guidance it has with the rules
Well the other options are the gooner gacha games like Mahjong Soul and Riichi City lol
Personally I play on Mahjong Soul because apart from Tenhou that has the most populated PvP with enough players in each rank + it's a butter smooth experience with all the small features. And I love the special modes like Battle of Asura
I design games and have been working on a Red Riichi variant where one of each number is red and this drives scoring instead of all the myriad of Yaku. All the Yaku are hard for beginners to onboard and a lot of hands have to good path to an interesting Yaku and just depend on luck to be able to call Riichi. I'm still testing it but I find it more interesting.
I also have a card game version that implements some of these ideas (although it doesn't have a Furiten concept).
Personally I'd say Mahjong Soul is the best riichi client out there, that's where I play https://mahjongsoul.yo-star.com/ Extremely streamlined, good QoL features like tile highlighting (dora too), showing waits and options when you are tenpai, custom lobbies (so you can play with friends), and a pretty robust online ranked system. There is a good tutorial too. The big downside is the gacha system which is purely cosmetic and doesn't affect gameplay at all but it can be a turn off for some people.
