Believe it or not you have answered your own question - it is in the tutorial that you linked to - at 7 min 40secs - however if you zoom in on the tutorial video in your browser you can see it clearly.
Click the Spectral view button on the right of the ACL window to go straight in the Spectral Cleaning mode.
I see what you meana now - the 'classic' view is vaguely mentioned, on the Magix website for ACL, and gives me the impression that it is no longer available as you have found.
I agree that ACL 2013 has lost the most useful features of the Spectral Cleaning. First, when you click the Spectral Cleaning button in ACL 2013, the program seems to calculate the ENTIRE spectral display. This can take many minutes. Previously, the spectrum was calculated in a separate window, only for the zoomed portion of the project, in seconds. ACL 2013 appears to have lost the vertical (frequency) axis zoom feature as well. This was extremely useful for fine-tuning the cleaning of unwanted noises.
I'm not sure what improvements Magix added to ACL 2013, but for me, the loss of the Spectral Cleaning features has me going back to my previous version (ACL 15) for routine work.