Is the STi as it really as beefy as it looks?
For a consumer-level street car, sure. Subaru's unibody frames are extremely rigid, and are part of why Subaru scores so high in crash testing.
how much of the WRC DNA made it into the production version?
The color.
You need to understand that Subaru's rally team start with a stock STI, then literally tear it apart to the bare chassis and start over. While the unibody is left largely intact, it is braced like crazy all over, plus a full roll cage is added. The suspension is custom-designed by the team and tailored to the driver's specifications. The engine platform is a base STI engine, fully rebuilt from scratch, and most rally engines require full rebuilds after just a couple races. They are built to go 10/10ths for the duration of the race, not comfortably power a passenger car on the street for the next 200k miles.
The transmission is replaced with a close-ratio dog box for clutchless shifts, and a competition ECU is used to manage the DCCD system. While DCCD functions more or less the same in the production and rally cars, the aftermarket ECU gives the rally team more control over the DCCD algorithms.
Your owners manual outlines what the car is designed for. The AWD system is designed to maintain traction on paved roads in inclement weather, not for offroad rallying. That said, I was able to drive my car in many unpaved areas, but I did so at a slow pace and was very careful not to high center on anything as the ride height (especially in the newer cars) is quite low. With a proper set of snow tires, I passed Jeeps stuck in the snow on Forest Service roads (driving slowly and defensively). Their only advantage was a taller ride height when the snow drifts got too deep for me to continue.