The 82188 is a bus controller. If there's one present on the mobo, or, I would have guessed an 8288, maybe you need to swap? Tread real carefully there. But I have to ask, did you read the instructions? What do they say?
Ok it looks like your board has the bus controller. If you give us specific part numbers we can at least identify what chips we're dealing with. The tech ref, starting on pg.138 doesn't make mention of an 8288/82188. That's just the mobo section. It would be nice if the manual gave us, along with everything else, the schematics and artwork for the 8087 upgrade. I didn't look the whole thing over to see if it was there or not. I suspect not.
Did you pull the board and see if the computer could boot without it?