GCHQ? Who's that?
IIRC, the place hasn't been called GCHQ for years (if it ever officially was) although I've forgotten the "correct" name for it.
Whilst their statement is almost certainly excruciatingly correct, the devil, as usual, is in the details: What exactly constitutes damage to the UK or its "economic interests"? As an example, leaving aside, for the moment, questions of the legality of the activity, does this include pirating of movies or music? As you so correctly point out, they are not aiming to monitor *everyone*, just *anyone*. whenever they want. And if they happen to latch on to something they deem interesting and within their (gargantuan and ill-defined) remit whilst searching for something else, why then, it behoves them to look at it, right?
GCHQ has, for years, been a master of finding every tiny chink in the legislation which governs its behaviour and exploiting them to do exactly what its "customers" want, often without anyone else knowing about it. This is possible because of the nature of the classifications it applies to most of what it does. You can bet your life that the various Commissioners etc who are supposed to oversee its operations aren't on the lists whose codewords are part of the classification of the most questionable documents and information. And will, therefore, never even get to know they exist.
Of course, the place does do useful work and, to be fair, finding the right balance between accountability (and lost laptops) and the secrecy required for operational usefulness is never going to be easy.
The clever/professional crooks/terrorists/etc will just (multiple) encrypt stuff & use proxies etc, thus leaving the spooks blind to what they're doing anyway.