Hi,
I am not the 'Guest' but I wish you will excuse me for using your post to ask and answer some questions.
You said, "A gerund may very well take an article in English. On the other hand, not every noun requires one." -- I agree but only few gerunds can take an article I THINK. Only one that comes up (in my mind) is the word 'reading' but I am not quite sure it is a gerund in this context.
A reading you have done yesterday was good.
As to the issue (question??) of whether the addition of "that we have been suffering lately" would change anything in terms of the use of the article, I would ask "Would the following say any different or would they just affirm what you were trying to assert (as I see it)?"
Something has been designed to stop (the) unwelcomed intrusions to our lives that we have been suffering lately.
Here, I think 'the' is optional and it could just do without and I think the Guest was trying to say (as I see it) that 'the' are there for the sake of parallelism and also, partly due to (maybe wholly due to) the subsequent phrase "of tracks purchased online" and not particularly due to the existence of the clause "that we have been suffering lately."
Incidently??, I think it is appropropriate to say like this if we construe??(think of) the phrase "unauthorized copying and play back" as a single concept and it is to be thought of as a single action:
DRM has been designed to stop an (implied "action of" ) unauthorised (shouldn't it be "authorized"?) copying and playback of tracks purchased online that we have been suffering lately.
I think you can put 'the' if there is only one unauthorizing copying and playback of tracks purchased online that they have been suffering lately like this:
DRM has been designed to stop the (no implied "action" here) unauthorized copying and playback of tracks purchased online that have been suffering lately. -- Here, I am still thinking of the phrase "unauthorized copying and playback" in a single concept term.
Does all this make sense?