The words he specifically objects to are:
barbellate
veridical
apiarist
Manichean
hydrocephalic
immiserated
mancipated
synechdoche
applique
quiddity
I like most of them. To substitute a synonym would be a loss. I prefer journalists to err towards precise and uncommon words. As Charlie Brooker said on telly last night, you weren't put off Monty Python if you hadn't heard of philosophers they joked about, and you might be motivated to find out more.
Having said that, I think 'mancipated' is a little pointless. I didn't know what 'barbellate' meant. I looked it up after reading the letter, but not after reading the review. I don't usually bother to look up words; I just make a guess.