Reanalysis is when the structure of a word is misunderstood. It's when people assume that a word has a certain make-up which etymologically it didn't in fact have, and then proceed from there, sometimes creating new words and usages.
A good example is the word 'hamburger', that being a food from the German city of Hamburg, i.e.: Hamburg-er. But English speakers, familiar with the word 'ham', assumed that a 'hamburger' was a ham-burger. And from there they generated words like 'cheeseburger' and 'veggieburger' and, tautologically, 'beefburger'.
Similarly we have the word 'aeroplane' which American speakers reanalysed into 'airplane' and then started making words like 'seaplane' out of that misunderstanding.
It can even take place across word boundaries. For example, the word 'adder' was originally 'nadder' but 'a nadder' was reanalysed into 'an adder'.
This is usually something done by ordinary speakers, not 'serious scholars of language' although having said that 'serious scholars of language' have come up with all sorts of nonsense in the past. I suppose one example might be the affected spelling of 'hiccup' as 'hiccough', analysing the 'cup' as though it were some corrupted pronunciation of 'cough', which it isn't.
That's what reanalysis is. With regards 'outrage' I suppose what the text in the OP is saying is that it should properly have become 'ultrage' pronounce ult-ridge /ʌlt.ɹɪd͡ʒ/ but this didn't happen due to reanalysis. I don't think it's saying all that much, though.