They made a public request whose intent is at least partly to persuade people in the Middle East that the American government does not support the bigoted views of the filmmaker. The government has an entirely legitimate wish to dissociate itself from this film and dispel the perception that it is intended as a piece of propaganda.
They also asked the pastor not to do the Koran burning. If there is no implied legal threat, what is the big deal? The difference in this case is going after a third party host rather than the original poster.
They could have done lots of things. Using soft pressure in various ways is not something that's new to governments or generally detrimental or something that's ever going to go away.
I guess Obama could also have written an anonymous letter to the editor instead of having a speech announcing and advocating his jobs programs. But that's not how the real world works. Obama openly and strongly advocating X, Y and Z is not tyranny.
Instead, they made a public "request" whose intent was to put pressure on Google outside it's normal "review process".