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You can use Castle Game Engine to develop any applications, including closed-source.
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If you modify the Castle Game Engine units, you need to share your modifications.
How it works exactly: Following LGPL, people that receive your application in binary form can ask for CGE sources. If you didn’t modify CGE, just point them to https://castle-engine.io/ , you don’t need to host anything. Otherwise you’ll have to show your CGE mods.
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Other than that, you don’t need to share your code, regardless of how it is using CGE. Your game code is yours.
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The CGE code is covered by our copyrights. E.g. if you distribute the Castle Game Engine sources yourself (modified or not), you must clearly specify our copyrights to the original code.