I'm still new to DSP, but it seems like there is a huge gap between DSP theory and actually implementing algorithms on microcontrollers and DSPs. What area of engineering deals with interrupt service routines, timing, block processing? I can't seem to find a clear answer, and the boundaries seem a bit blurry.
This is a very good question.
As I see real-time systems, both theoretical and a practial subject there are different aspects that can be discussed.
If we are looking at issues of OS related issues, how interrupts are handled, which different microprocessor can do different things etc. than certainly https://electronics.stackexchange.com/ is a better place.
However, there are several questions about real time systems which will seek understanding from "control systems theory" and very algorithmic in nature - such as feedback loop designs etc. Such questions can be welcome questions here.
The crux i think relies on what you are expecting from the answer.