For web support (support cross platforms) you need to use libraries that do not use Java features such as reflection (Gson problem). If possible use libraries implemented in libgdx. In your cesecase, use [https://github.com/libgdx/libgdx/wiki/Reading-and-writing-JSON][1]Reading and Writing JSON.
There is always some peacepiece of platform specific-specific code. For this, write javaa Java interface class and implement it for every specific platform (also test it ;)). Pass this object throwthrough your game constructor in your core game. For more see: [https://github.com/libgdx/libgdx/wiki/Interfacing-with-platform-specific-code][2]
[1]: http://(https://github.com/libgdx/libgdx/wiki/Reading-and-writing-JSON [2]:For more, see https://github.com/libgdx/libgdx/wiki/Interfacing-with-platform-specific with Platform-codeSpecific Code.