Digital Signal Processing is a fundamental field in electronics and always will be as long as we have any form of electronic communication or signals. Most modern active electronics parts (even many power converters!) fall under either analog or digital signal processing so it's a core field of study. Technically, your CPU is just a power hungy multipurpose DSP but we don't refer to them as such to maintain precision in the jargon.

Proper DSP chips are highly specialized processors just like GPUs except they contain lots of silicon for low latency and low power math. Your wifi or cellular radios, for example, are highly specialized DSP chips that only deal with a few protocols.

Hmm not sure what you mean by relevant here. I'll take a crack at my interpretation: Is DSP still relevant - undoubtedly yes. Is the book still relevant? Because it focuses on the underlying theory and concepts and not so much on language specific implementations, I'd say yes to that as well.

Not sure whether you're asking whether DSP is still relevant (I think it is) or a textbook published in the 80s would be relevant. I imagine such a book might talk a lot about the hardware and software available at the time.

HELL YES!