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I would say your answer is pretty good.
Some corrections (uppercase to show the corrections).
"Me gusta jugar A videojuegos".
"desarrollo de juegos" is fine as it is, without a definite article prepended. One caveat is that you have changed "videojuegos" by "juegos". "juegos" is not used for computer or console games. Use "videojuegos" for those.
Instead of "y porque estudio un montón" use "y por eso estudio un montón.". You want to say, "as a consequence of x I have to do y". To say that, we say "por x tengo que hace y". As x is the subject we have been talking about, you can substitute it by "eso".
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