In this question, 中 is a "postposition." We'd call it a preposition, but since it shows up after the noun that it applies to, 过程 (process), it's technically a postposition. It means "middle" or "middle of."
In English, we can omit "middle" when we say "in the process of" because "middle" is implied already. While we technically can omit 中 in Chinese too, it sounds far more natural to include it. From my experience, the only time native speakers don't include the 中 after 过程 is when 过程 implies an entire process from start to finish. For example: 学语言的过程很困难 (the process of learning a language is very difficult).
I hope my answer helps. Please let me know if it doesn't.