MTV as a music video channel was dying long before the Internet was a significant factor. Non-music programming started creeping in during the early nineties when programs like "Real World" first appeared. Ten years later, it felt like the music videos had become filler between other programs, and that is long before most people had connections that would support streaming music videos over the Internet.MTV was killed by the internet. The same thing killing radio. Habits have changed the model across the board. Radio, TV.
In the end, it turned out that running a cable network that was essentially a radio station with pictures was just too "niche" and the audience size too limited, so management started branching out in hopes of attracting a larger audience who would tune in for specific programs. It's the sort of dilution that turned out to be pretty common in the cable TV world -- looking at the utter crapola that they air today, it is hard to believe (for example) that TLC actually started out as an educational channel (TLC originally stood for "The Learning Channel") and that Bravo focused on high culture before heading down market.