The two most important chips in a game console are the CPU and GPU. In the Atari 2600, the CPU was a cut down version of the 6502, a very common low-cost microprocessor. The GPU was the TIA, which was manufactured for Atari by several chip companies, as detailed in the answer to Who made the Atari 2600 TIA video chip?
When competitor Coleco introduced the Colecovision, they also introduced an 'adapter' to make it compatible with 2600 games, which effectively consisted of a 2600 console in an adapter form factor. Presumably for this, they purchased TIA chips from one of the manufacturers thereof.
I am surprised that Atari didn't get to object to this on the grounds that they owned the intellectual property rights to the TIA. Why not? If they didn't own those rights, how did that come about?