The reason the jumping in this run looks so slow is because Mario does not maintain momentum and the minimum jump height is much higher. This game is known for being notoriously hard to control, and it can be seen well here. This was a very simple TAS that did not take an insanely long time to make. This is not perfect though You could probably save around 50 frames.
Being able to go straight to Bowser's castle was a programming oversight and was only in around 50% of the carts that where released. Other than that not many glitches are used in this run.
A video will be added soon
Emulator: FCEUX 2.2.2