My Android ver is 4.4.2
Trying to manage the contacts list, the options are as follows:
People => Me => Contacts to Display => Customize => Define Custom View
and then it lists, as the only options, my accounts: Skype, e-mail, Google+ (which I didn't activate, but they list it anyway).
My only choices are to include or exclude each account as a whole, except on the e-mail accounts, where there is option to select My Contacts (Current selected), Starred, Friends, Family, CoWorkers, All Others. No option to select Phones only.
(This is a Motorola Phone, sold while Motorola was a Google company; so I believe this is stock Android - no Motorola customizations)
I think you may have gone down the wrong menu path; unless it is really missing on your OS version. My "Only contacts with phones" option is not under "Contacts to Display" path. It is actually under "Settings" right below "Contacts to Display". The first box under "Settings" inside "Contacts App" is "Only contacts with phones" check box.