what is darknet and why is it needed for YOLO object detection?
https://pjreddie.com/darknet/ is their website...

I cite : 

"Darknet: Open Source Neural Networks in C

Darknet is an open source neural network framework written in C and CUDA. It is fast, easy to install, and supports CPU and GPU computation."

As to why they used that, well it's open source and in C, which are good points and seems to be performant (see the graphs in your link and associated paper). But the main point seems to be about history. The darknet project seems to have started in 2014. Were tensorflow / keras available and perfromant at this time in the first place ? Even if they were why should they use keras / tensorflow ?