To me, "a nasty abomination of a product space" reads like "a product space which is a nasty abomination". The "only related ..." bit is good, but it comes much later in the article; it's the early bits that I think are liable to confuse.
I do appreciate, by the way, that explaining nontrivial mathematics to anything other than an audience of very good mathematicians is really bloody hard!
That's a good point. Maybe the word "adulteration" or "bastardization" would be better? Or maybe to avoid odd connotations I should just say it in long form: taking a mathematical machete to a product space and making it nearly unrecognizable.
I do still think, despite what many have said, that a comparison and distinction needs to be made between usual products and tensor products. I think "modifying a product space" happens to be a different way of thinking about it (maybe not the best way), and for what it's worth it helps me keep track of the damn things.
I do appreciate, by the way, that explaining nontrivial mathematics to anything other than an audience of very good mathematicians is really bloody hard!