Let's assume I am wrong (I am sure, I am not but just to keep things interesting).
Use millis and measure the time you spend on each stage of your code. Then you can see which part is taking most of the time.
I also checked the youtube links. Firstly they do not look that responsive at least to me. But also the interface is important too. for example on some LCD controllers you can have 16 i/o connection for data bus and controlling signals and that would be way faster than using SPI (SPI has only 2 or 3 wires depending on how it is used and chip select which is not even counted). Moreover the SPI frequency is one thing that can affect this as well. Arduino (the non arm ones) do not offer a very high speed SPI compare to what is available in SPI world. but then again the LCD controller should support that higher frequency setting.