> Actually, Tengen made games for Nintendo just like any other developer at first,
> their games were regular grey ones like all the rest.


Actually, Nintendo manufactured all NES cartridges themselves, both first-party and third-party. Third-Party developers submitted the game program to Nintendo, who then burned it onto ROMs, adding the appropriate Mapper chipset the developer specified.

This was all a part of the license agreement and Nintendo's "Seal of Quality". (The Seal was meant to indicate that Nintendo can confirm the game/peripheral works, because they manufactured it or tested it.)

Eventually, some third-party companies grew tired of this (or were unable to pay the licensing fee) and made their own carts. They couldn't outright mimic the patented design of Nintendo's cartridges, so they came up with their own creative shapes.