Yes, a PS2 has a 128 bit processor. No, it has nothing to do with anything being on or not being on the chip, like video.
All this means is that the bus allows for 128 bits of information to pass in a single clock cycle. It does not mean the processor in a PS2 is more powerful than an Intel compatible PC, nor does it mean that it's faster. It's just how much information is passed in a single clock cycle.
And, for the record, SGI, SUN, Alpha, and many other manufacturers have been making 64 bit and even 128 bit processors for years and years now. They're just not Windows machines so you guys had no clue they existed. Transmeta even has a 256 bit chip out.
Compare a PS2's bus to an Intel compatible PC's bus. Then compare registers, caches, instruction sets, and all other aspects that make up the performance of a processor. Someday you guys will find out that bit size and even bus speed does not a processor make.