The main card gamist/WotC influences I see in 5E, relative to 2nd edition, are that:
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Capabilities are defined primarily in gamist terms. WotC will think up a mechanically-cool ability like Bardic Inspiration, Cutting Words, give it a snappy name per #1 and a place in the action economy (bonus action/reaction), and give absolutely no thought to roleplaying considerations such as just how exactly a bard is using one mouth simultaneously to give an inspiring speech to a companion (bonus action Bardic Inspiration), insult an enemy (reaction Cutting Words), and cast a spell (action Fireball) using his kazoo as an arcane focus, all in the same six seconds.
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There's an implicit structure to capabilities, and the writers avoid going outside the box. Capabilities are strictly-defined to avoid potentially upsetting mechanical balances, even when it's probably not necessary.
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All three of these aspects remind me of card games.