I know that the question is from March 2022 and I am answering this on 31st January 2023, but I did not want to leave it alone and maybe someone else will at one day search for a solution to fix the same problem, so here I go:
Bad news first: Unfortunately, the intro breaking down in the middle is a bug that has never been fixed and even now, with the game patched to its most up-to-date status by GOG (Version 1.5.5), this very bug is still included and likely never to disappear from Rise Of The Triad (2013).
Yet, do not lose hope, as all the videos in the game are obviously stored in the game’s files and since they are .bik files you can watch them easily with video software, for example with the Windows Media Player Classic or with the VLC Media Player. There may be more video players that work, but these are the two ones that I personally use and that can play the .bik files of the game without any problems.
To find the intro and all of the other videos of the game just do the following:
Open the Windows Explorer and go to the directory on which you have installed Rise Of The Triad (2013), whose standard folder name is ROTTGame. Open this folder, then open the folder named Movies, double click on the file with the name ROTT_INTRO.bik and enjoy the intro.
I know this solution is as simple as one can go, but it is the only way to watch the intro in all of its glory, at least from what I know so far. After I have installed the game for the first time the intro played flawlessly to the very end, but since then it always broke down in the middle as well, when the bazooka guy from the Triad is ready to blow up the HUNT team’s boat. At one time the intro even broke up at least two seconds before that scene. Seriously, the game is very good and if the developers would have spent just about a few more months to get all the problems fixed it could still be alive today.
