Plausible?
Even the author has stated that it only goes that way because: (a) every single decision point breaks the way it does to get the desired end. There is not a single instance of a decision point going in such a way as to make achieving the desired end harder. (b) Those who might be expected to interfere with movements towards the desired end result simply do not take any action to prevent things going against their wishes. The forces of inertia and opposition basically don't exist. (c) Known personalities get adapted and shifted out of all recognition. (d) A near complete absence of understanding of the Troubles and the interweaving of the complexities. The only reason, for example, why the IRA placed the Westminster bomb where it did in the tale was "because it was necessary to achieve the desired end result".
Plausible? Not even the author claims plausibility.
So I almost included a sentence in parentheses caveating what I said and apparently it was a mistake of me to decide that was unnecessary.
Yes, the timeline relies heavily on a "worst case scenario" chain of events which are highly improbable and almost impossible when viewed as a whole. But they all follow on from each other as things which plausibly *could* have followed from the previous incident even if other consequences were more likely. As such the TL as a whole doesn't require alien space bats or massive suspension of disbelief.
The timeline is implausible because it relies on the worst possible luck which is, obviously, authorial artifice. However, it's not unbelievable and doesn't require much suspension of disbelief because, to reiterate the above, the events and reactions are all ones which you could conceivably imagine happening despite their unlikelihood.
After all, real life history often features incredibly bad luck and the worst possible reactions to it to the extent that, if it were fiction, we'd call it unrealistic; for instance, the Plague of Justinian would seem ridiculous if a TL had introduced it as a deus ex machina to end the resurgence of the Eastern Roman Empire.
Most alternate histories are fun "what ifs" following a pre-decided narrative. For me If Gordon Banks Had Played is chilling not because I think the IRA were just a football game away from blowing up half of Britain's MPs but because the TL does a good job of exploring how, given a worst case series of events, a supposedly sane and stable democracy could spiral into increasingly extreme reactions and totalitarianism. And that is something which it's a common British conceit to imagine "could never happen here".