I missed the discussion about Ponies playing card games but I have put too much thought into what
Yu-Gi-Oh! archetypes they'd use to wait for another opportunity.
Twilight: Cyber Dragons. Why? They are all machine based and Twilight is scientific, as seen in Feeling Pinkie Keen. Also Cyber Dragons are all either Light or Dark. Twilight is the time between night and day.
Rainbow Dash: Crystal Beasts. Why? They are all about rainbows, the seven Crystal Beasts are each a different colour of the rainbow and their trump card is the Rainbow Dragon.
Pinkie Pie: Arcana Force. Why? Arcana Force are based on Tarrot Cards. Pinkie Pie can predict the future. Also every Arcana Force effect is based on flipping coins which like Pinkie are random.
Trixie: Dark Magicians. Why? Dark Magicians have great lock down effects. Secret Village of the Spellcasters prevents Spell Cards, Magician's Valkyria prevents attacks and Dark Sorcerer can negate Trap Cards. Trixie's performances rely primarily on making others look bad by limiting their abilities rather than overcoming them.
CMC: Elemental Heroes. Why? Their are three variants of Elemental Heroes; Warrior, Nature and Neo-Spacians. There are three Cutie Mark Crusaders. Scootaloo would need to use Neo-Spacians as one of their best cards is Rainbow Neos which involves fusing Rainbow Dragon (Rainbow Dash's trump card) and Elemental Hero Neos together. Also expanding on the Hero aspect, there are three variants of Hero; Elemental, Destiny and Evil allowing for further diversification.
Fluttershy: Beasts. Which ones? I'm uncertain, maybe Green and Yellow Baboons, Blade Rabbit. But other cards would be My Body as a Shield, Prideful Roar and Astral Barrier. Cards that protect her monsters at the cost of her losing life points.
AJ: Plants. I don't know which ones.
Rarity: I have no idea.