[AnotherUnixGeek]

Watching the Bengal offense from that '69 season you would never believe you were looking at what was in fact a Bill Walsh offense. It was the complete antithesis of what you saw in San Francisco.

He worked with what he had - coming into SF, neither Steve DeBerg nor Joe Montana had big arms, the 49ers had no running game to speak of, and their OL was athletic but undersized. So the short-to-midrange passing game that the Bill Walsh Offense became identified with.

[Cyropaedia]

Actually, after they discovered the extent of Cook's injury, they traded for a veteran QB named Virgil Carter. Of course, Carter barely had a fraction of the natural talent that Cook possessed. Walsh realized that he to completely revamp his offense and tailor it to Carter's abilities. Carter was a savy player that got by more with his wits that athletic ability. Walsh installed a lot of short, high percentage throws, screen passes to the backs, etc. By his second season, Carter wound up leading the league in passing percentage, and finished the year as the highest rated passer in the AFC. And thus, an offense was born. The "West Coast" offense actually began with the Carter and the Bengals.

That's one other thing that most people don't know : Walsh had always hated the term, "West Coast offense", because that's not where it originated.