OK, I've done some poking around on the Simulink web site. It appears that it does indeed automatically download a sketch into the Arduino.
It also appears that the digital output example that works for you is the first example "Getting Started with Arduino Hardware." You posted the block diagram for this model - if you read the last sentence of the portion of the image you excluded, it states "This model runs as a standalone application, independently of Simulink." So there is no communications between Simulink and this model. That is apparently why it works.
The other models require communications between Simulink and the model, and you are trying to do this communications over the network. None of the examples on the page you linked specifically mention compatibility with the Yun. Simulink has a hardware selection field that includes the Yun, but I suppose that is only configuring how it talks over the USB port and how it communicates with the Yun's bootloader.
Digging deeper, the "Modeling" page has links for the common modeling blocks. It also has links for Ethernet Sheild and WiFi Shield blocks. I don't see anywhere that it mentions Yun networking blocks. Remember: the Yun is NOT the same think as a regular Arduino with a WiFi Shield - the networking is completely different.
At this point, my best guess is that while Simulink does support the Yun hardware, it only goes so far as supporting the common model blocks, and does not support the networking abilities. You can probably get any of the stand-alone models to work (like you can with the basic digital output example) and you can probably get models to work that communicate over USB. But it doesn't look like Simulink supports the Yun's networking abilities, so anything that tries to communicate over the network (wired or WiFi) is probably not going to work.
This doesn't sound like a Yun issue, it sounds more like a Simulink limitation. Given the lack of response to this thread by others, I don't think you will find a lot of Yun users here that also use Simulink (probably because the Yun networking is not supported?) You will probably have better luck pursuing this task with the Simulink folks.
To get this to work with Simulink will probably take some custom programming on the Yun, but if Simulink does all of the coding behind the scenes, that may be impossible (or at least very difficult.) It sounds like Simulink was designed to use an Uno (or more likely it prefers a Mega2560) with a WiFi Shield. If you want plug and play operation, you are probably best sticking with the hardware that is specifically supported by the examples.