need? or want? openGL has been faster and more advanced than DX for quite a while now, now i'm not a huge fan of tesselation (its a cover for bad artwork in some instances, and when used badly it creates even worse artefacts and performance decreases) but OpenGL had it first by a long time.
Also i'm not going to list other engines in here, but searching mit licence and game engine in combination should very quickly point you to a number of open source engines you dont even have to give a passing mention of credit for, to such an extent that you can take an MIT licensed product, rename it, re-badge it and actually sell it as your own game engine. Of course the dev community is too savvy to let that go without comment, but its still possible :p
The only reason i even brought it up in the first instance is that there's a lot of buzz about AI and pathfinding being missing or needing work (i'm nopt eve sure theres an A* algorithm at play here, AI seems to stand static if theres an object between it and you) and recast has been used on a fair number of quite big games as well as more than one game engine, and does more than any other pathfinding product on the market and is still being constantly worked on, reinventing the wheel is never a smart play when free wheels are available, a decade or go there was no options, maybe even 5 years ago, but now? you can build a custom game engine in 6 months for your own games if you have that level of experience and know how.
As for potential parts of game engines, for pathfinding you have recast as mentioned.
Rendering: Ogre, bgfx, allegro, SDL
2 (i know the last 2 not strictly rendering engines, but as a relatively simple interface to DX/GL dey is close :p )
Model Importer: Assimp (which will probably be needed anyway since .x has been deprecated for years; gosh, even .dbo is more common than .x lol)
Physics: Bullet (OMG gameguru already uses this, which makes sense given all the previous comments about how OSS is evil and cant be used..) ODE, Newton there is also Tomahawk, very old but functional :p
There are also lots of other generic tiny libraries that you can use if you are building your own engine/game LibCg , zLib, LibRocket, SQLite, stb just a few ive come across, so BSD, Zlib MIT all the nice goody licences keep a look out for those.
GPL is pure poison, avoid, seriosly if you see a GPL zealot, cross the road, do not engage in any form of conversation.
LGPL, is a lesser evil, yet in some ways, this is the backstabbing friend of the in your face GPL, can be used if you have a lawyer brain, or better still, a lawyer friend.
Also theres a another thing i meant to mention regarding rulfys earlier comment, even the evil GPL library only has certain limitations, for example, products of a GPL licensed software are not GPL licensed, otherwise every blend file and blender model would be unusable and useless