I don't think Tim Vine is particularly proud of his reaction to The Last Post but he has been honest and inappropriate responses like that may strike a chord with some of his audience.
The Last Post is an evocative and emotional piece of music, in or out of context, and most people will feel a need to express that emotion. When I hear it, I can feel myself welling up, bottom lippy all a-quiver and I may or may not be able to control this into stiff-upper-lip or I'll head for a full-scale blubbing. But I can do that in public, I'm a girl and girls are "allowed" to cry.
However, he and his friends were boys, children with all manner of hormones surging uncontrollably round their bodies and we all know that boys are not "allowed" to cry. But the emotion has to come out somehow, so it comes out as suppressed laughter. It is a reasonably common reaction to powerful situations; common enough that Tim Vine's piece was not particularly funny but it does have a ring of truth about it.
So, to Bootneck and the Royal Marine, please try to remember what it was like to be a teenager 20-40 years ago!
Cheers
Whirls