Custom Flash players were actually relatively common in game development during the mid to late 2000s, as Flash provided a ready-to-go authoring solution for UI and 2D animation that artists were already familiar with. Autodesk's Scaleform was probably the most popular implementation but a number of AAA developers had their own in-house libraries similar to Doom 3's; some of them, such as Konami's "AFP" [1], are still in use to this day (the latest game to use it, Sound Voltex Nabla, was released last month).
You could call it Lightweight Scaleform. This same codebase was used in RAGE.