Why does SQL Server use this index?
While I cannot confirm this with any official documentation, the reason must be based on the total size of included columns and the cost.

With the test i conducted, the indexes with 10 columns and 3 columns had exactly the same cost and logical/physical reads, which I assumed to be the same with the original poster's environment.  I gradually increased the size of the 4th column, and at certain point, the opimizer started choosing the 1st index for the 1st statement.  The table used had about 55k rows.

This only shows an anecdotal evidence and a theory on certain behavior of the optimizer.  I hope  someone who really knows the meanism of it will explain us all why, if this theory isn't correct.