Yes, Gameplay Programmer is a specialization. Gameplay Programmers are the engineers who work directly with designers to make the designs actually work in game. This primarily means writing code to make the systems and rules that the designers come up with work.

Gameplay programmer goals tend to be building systems that allow designers to create new content. This often involves building and supporting tools to allow the designers to create, edit, and tune many different individual instances of a specific kind of content - abilities, spells, items, enemies, quests, etc. Thus, a gameplay programmer might build an item editor that would allow an item designer to create many different items. This can scale up to enormous core gameplay-driving systems, like Shadow of Mordor's famous Nemesis system, Prince of Persia's Time Rewind system, or Street Fighter's combat.

Gameplay programmers are not particularly high priority when it comes to layoffs. Engineers tend to be more expensive and marginally more difficult to hire and vet than other fields like QA or production, but gameplay engineers are absolutely not the kind of unicorns like technical artists, engine programmers, graphics programmers, and the like. There's always a need for senior gameplay programmers when it comes to standing a game up at all, but you only need as many gameplay engineers support the designers to build the content that production has scoped.
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