Whilst fatigue may have affected their "strategic" thinking processes, it should not have blocked their response to the safety net provided by the EGPWS alarms.
Without being at all judgemental, asking for the short-cut to runway 21 probably seemed like a completely reasonable request at the time. They were tired, it was a long day, and saving 5 minutes would be good news all round. The contribution of fatigue need only be a small error in the mental arithmetic that we do all the time - when ATC asks "can you make it from there" and you do a quick time/altitude/speed calculation in your head and say "yes".
However, as time passed and the evidence started to appear that the quick time/altitude/speed calculation had gone wrong, they pressed on. Even that poor judgement wouldn't be the end of the world. But, as soon as the aircraft starts saying "whoop, whoop, Pull Up!!", swiftly followed by most of the other announcements in its vocabluary, that is meant to tell you that this is never going to work.
You don't need to exercise any judgement at that point, and it doesn't matter how fatigued you are, because the Ops Manual (and all the training you ever had in the simulator) tells you that what happens next is not discretionary. You add power and pull up.
The breakdown in this incident wasn't the poor decision making that led them to try for the short cut. That was just a bit of a mistake. The error was the point where all the alarm bells went off - and they decided to keep going.