Can anyone explain why in the world they would use an electroluminescent light instead of a simple LED?

someone in the comments theorized it was at first supposed to be a full-fledged front light but the design changed and they just used whatever hardware was already there to power the logo

You don't use EL as a "full fledged front light", they don't have the lumen output and need a lot of support (high voltage) to produce what they do.

In the video you can see that the LED lights the logo less evenly than the EL lighting. While that's not important at all, this might be the reason behind this odd choice