It's easy to get discouraged but at some point you'll hit the "oh, I get it" moment. I got the Xilinx RTOS + TCP/IP to work in a few hours but am still baffled by the Altera SoC tools after a week of head banging. So I can sympathize.

However, it looks like the "Board Update Portal" example uses a NIOS II soft processor. The user guide does not say what operating system and TCP/IP stack is used, but I'd guess they are using niche stack TCP/IP stack and uCOS II.

The NIOS II tools and training are actually pretty good. Not sure why Altera chose to have useless garbage tools for their latest and greatest SoC chips and great ones for a soft processor, but I don't run the world. In fact, as I remember, if you go through the NIOS II training, one of the examples is how to create a TCP/IP example.

The user guide says the source code for the "Board Update Portal" example is in the:

<install dir>\kits\cycloneIVGX_4cgx15_starter\examples

directory. There will be two kinds of source code. The HDL code to create the hardware (including the NIOS II processor). But there should also be C source code showing how they run the web server. The TCP/IP stack is in C code running on the processor. It will make alot more sense if you work through the NIOS II online training.