Hi, welcome to the forum.
I hope that you don't get disappointed in Arduino, but that is not a hologram and it is not a project for beginners.
It is just a 2D display that displays video.
The frames to make something rotate are already calculated on a PC. The device just plays the video. The "holographic" claim is fake. They call it a "holographic effect", well, then I call it a fake effect.
As a beginner, you could start with a basic Arduino board. Those boards are too slow for such a project.
At Adafruit, they have a lot of tutorials. Tutorials for beginners, tutorials with ledstrips, and so on: https://learn.adafruit.com/
[ADDED] It seems to spin at 40 cycles per second. With an image height of 512, suppose the led update is 2000 per cycle (just a wild guess). So the leds should be updated 80000 times per second. Looking at the picture I guess that there are 320 leds in the bar. With 24-bit RGB values, the data rate would have to be 614 MHz. That is too high. They are cutting a few corners, but I don't know how they did it. The LPD8806 led driver can go up to 20MHz for the clock. Perhaps they don't use a single channel, and I think that they must use a DMA channel for the signals.
Nevertheless, the result is really neat, showing a picture without seeing a display. They did a good job for making such a fan display. It is also expensive. They make larger ones for even a better result:
Same question about the same fan display: https://forum.arduino.cc/t/diy-led-fan-display/628727