Afaik you can't do that, what you can do is use the same assets in your engine, if they are made by you and not just a modification or derived from Crytek assets. And i mean all basic assets, like, models, textures and sounds, for the most part, all assets generated by the Cryengine editor cannot be used outside of Cryengine. The AI custom code and the script code is not yours, even tho you write it, you used the engine Lua/c#/c++ methods/functions to write it so, there is underlying code from Crytek in there.
The best and safe way for you is to forget Cryengine entirely and just develop your engine and game at the same time, inhouse, it will help you optimize it better to the game you are making and will save you from legal problems that could arise from using Cryengine in that manner.
2.4. Restrictions on Use: Crytek reserves all rights not expressively granted in this Agreement. Without limitation, Licensee shall not:
distribute, sublicense or exploit in any other form:
the CRYENGINE (except for the Redistributables), e.g. as a stand-alone development engine;
the CRYENGINE Documentation;
the CRYENGINE Tools;
you are not allowed to combine CRYENGINE with code from other game engine providers ;
What you want to do can be considered a exploitation, use Cryengine tools for your own benefit (use their tools to make games for your engine).
By taking AI/script/etc code from Cryengine and making it work on your engine, IMO that falls into the "you are not allowed to combine" point of the restriction on use for Cryengine.