c# async without await

In documentation here: http://msdn.microsoft.com/en-us/library/hh191443.aspx it indicates that:

If an async method doesn’t use an await operator to mark a suspension point, the method executes as a synchronous method does, despite the async modifier. The compiler issues a warning for such methods.

I believe this is the warning:

This async method lacks 'await' operators and will run synchronously. Consider using the 'await' operator to await non-blocking API calls, or 'await Task.Run(...)' to do CPU-bound work on a background thread.

Then, in a different, referenced link, http://msdn.microsoft.com/en-us/library/windows/apps/hh994635.aspx, the example it shows is as follows:

public class Example
{
    // ...
    private async void NextMove_Click(object sender, RoutedEventArgs e)
    {
        await Task.Run(() => ComputeNextMove());
        // Update the UI with results
    }

    private async Task ComputeNextMove()
    {
        // ...
    }
    // ...
}

Here, I'll assume that ComputeNextMove is basically a synchronous method, itself, not calling await. That then would seem to contradict the issuance of a compiler warning (unless it's a bad example...)

If I'm not calling a .net Async method at the END of my asynchronous call stack, like HttpClient.GetStringAsync and I do want to implement some concrete "long running" synchronous logic, is there a more proper way to do it?

Perhaps my assumption is incorrect, and ComputeNextMove could be declared as private void ComputeNextMove() which would yield no warnings.