1st a/c cleared for takeoff, I assume 'immediate takeoff' and I assume 1st a/c was asked in advance if they were ready.
Correct so far - but the problem was the 1st a/c
then proceeded to taxi part of the final distance to rwy at 5 kts - and was
not actually ready due to not yet receiving "cabin secure" notification. They had just "hoped" they'd actually be ready when reaching the threshold.
When asked again if ready for immediate TO, and replying "negative," transmission was garbled and ATC heard "affirmative."
Airport surveillance system issued an alarm due to insufficient spacing - tower cancelled TO clearance, but
that transmission was stepped on and 1st a/c did not hear it. But by that point, fastest way to get a/c 1 out of the way of landing a/c 2 was to proceed with the TO.
Issues were poor communications (situational and technical), and triggering the surveillance alarm made it a "official" event that therefore had to be investigated/explained.
I might fault the crew of a/c 1 for accepting an "immediate TO" clearance they were not really ready for. If you
aren't ready - right now! - you shouldn't say you are.
But the radio problems closed off opportunities to rectify the situation before it became an "incident."