I've watched the video of these 2 women cooking and discussing this dish before. It has been discussed elsewhere on the forum and raises some interesting points.
1) They say in the video that British Chicken Tikka Masala is just Butter Chicken (Murgh Makhani) with a different name.
However,
2) Most Butter Chicken recipes do not use pre-cooked Chicken Tikka, just chicken. (a possible differentiation between the 2 dishes as far as BIR is concerned), so is the OP recipe here one or the other or a hybrid?
Also discussed elsewhere on the forum:
3) Some Butter Chicken recipes do not actually have any butter at all. This has been discussed before and stems from the definition of Makhani gravy as having a buttery mouth feel without necessarily containing actual butter but ghee, oil and cream.