Why did the delegates who wrote the American Constitution select the indirect elections of the president by the electoral college?

The Electoral College was set up as a means to establish, as you said, an indirect method of presidential elections.  The rationale for this, while not simple, is fairly straight forward.

1. At the time of the founding of the nation, there was limited eligibility for voting: being white and a land owner were the two main necessary requirements that prevented well over half of the nation from voting.

2. At the time of the founding of the nation, the literacy rate for the nation was not near the level of our modern rates today.  Because of this fact there was some fear that a direct vote could be manipulated by emotional appeals to the majority that might be informed enough to avoid being swayed.

3. At the time of the founding of the nation, there was some fear of rob rule on the part of the public.  The leaders of the Revolution had spent a great deal of time, money, personal sacrifice, and reputation to free the nation from England and they wanted to have more say in the early founding of the nation.

By setting up an indirect selection process of delegates for the Presidential election and as the selection of US senators, these men felt that the nation would be able to "grow up" under limited mob rule mentality.