The lsmod output shown in your post #16 shows this driver to be loaded. As mentioned in post #15, it should load on boot, since the kernel sees it.
The next step is to ensure that the firmware package: firmware-realtek, is installed. This package provides firmware blobs which the realtek drivers needs to run, so you need to install that package. After it's installed, it's wise to reboot to have its blobs loaded. There should be no need for any modprobe commands at all.
I'll search for that - but two questions:
1. how did you know to use that specific hex number 0280 for the lspci command, and
2. the git hub page didn't mention anything about a realtek firmware install - to that, I wanted to know: is that a requirement for any and all driver installs (which might explain why the author didn't mention it, if they assumed that everyone would know that was a requirement)?