Please tell me what part of the source code infringed copyright?
The statement calls out instances of the running application infringing copyright. Nowhere does it say the source code was infringing copyright (and I am not sure how source code could unless it was either stolen or had the lyrics to "A Whole New World" in one of the comments.)
Which means the DCMA notice was targeting a tool of potential infringement not infringement itself.
"Please tell me what part of the source code infringed copyright?"
Judging from your question, your confusion about why this is illegal stems from two problems: you're unclear on both the law in general and the charges in particular. In this case, there is no complaint that the code has been improperly copied from someone else. Indeed, the code may well be an original work, freely distributed by its author, and being used in full accordance with his wishes.
However, copyright law covers more than that. Here, the complaint is that the code exists principally and primarily to violate the law, which is a violation in its own right. In this regard, publishing it is a bit like distributing sawn-off shotguns, which are generally illegal regardless of what's being done with them.
Why do you keep saying "potential infringement"? Are you actually so unaware of the details of this situation that you are unsure whether anybody watched content through Popcorn Time without authorization from the copyright holder? There have been users in HN comment threads who admitted to doing so, so you can set your mind at ease that there was actual, non-potential infringement here.
The statement calls out instances of the running application infringing copyright. Nowhere does it say the source code was infringing copyright (and I am not sure how source code could unless it was either stolen or had the lyrics to "A Whole New World" in one of the comments.)
Which means the DCMA notice was targeting a tool of potential infringement not infringement itself.