Is it possible to replicate ...
These are two different software. Software like these can change a lot from version to version. So you can't assume that you'll be able to "copy-paste" code from a game to another. So no, don't expect it is possible.
Fifa 14 has been taken out from play store, so I think it is fine if this mod is made.
This does not remove the license that is attached to the software. You would need to look at the specific licenses that come with the games, but here is an excerpt of what is currently available online (emphasis mine):
You may not access, copy, modify or distribute any EA Service, Content or Entitlements (as those terms are defined below), unless expressly authorized by EA or permitted by law. You may not reverse engineer or attempt to extract or otherwise use source code or other data from EA Services, unless expressly authorized by EA or permitted by law.
So no, even if it has been taken out from the store, you cannot dig into the app.
And yeah, this is only for non commercial use.
This does not matter, a license is a license, and a copyright is a copyright, money involved or not, you are bound by the license, and you don't own the copyright.
I have both games obb and apk files. I am able to access all the files of both the games.
I suspect that you have assets and binary files. The code, what glues the assets together and displays it on your phone, is compiled; you would need to decompile it and figure out what is going on. It could probably be done. But the license does not allow it.
What can you do? Write a new game including the features of both; try to figure out what are the elements that made you enjoy both games, and try to replicate them in your new game.