"Which programs generate object code? IMO, it's a compiler."

Hmm, re-reading my previous post, I somewhat missed the point of that question. Sorry.

In fact, the Keil Compiler, Assembler and Linker all generate Object code (in OMF-51 format, or Keil's extended variant) - the Compiler & Assembler generate relocatable Object; the Linker generates absolute executable object modules.
See the introduction to the Linker/Locator in the Keil Macro Assembler and Utilities manual.

"How does it know that the code it will ganerate results in more than 2K?"

That needn't be difficult: it could just keep generating object code, counting the bytes as it goes, and abort as soon as it exceeds 2K!
You could easily try it and see