Is there a word or a special phrase in English to describe the curvy upper lip that some people like Rio Ferdinand have?

I don't think there is a technical name to describe R. Ferdinand's shaped lips. As you pointed out that they are quite rare, and unless one day they become a medical condition (how likely is that going to happen?) or a new trend for that particular upper lip reshaping constraining plastic surgeons to agree on a name, then there's probably no need to classify them differently from a Cupid's bow mouth.

One way round you could overcome this obstacle is inventing a new name yourself, if it's any good the listener will know exactly what you mean. I thought up a few just for fun:

• a Rio pout
• lips alla Joile
• enhanced curvy lips
• kissiest lips
• bouncy lips (think bouncy/cascade slide in a funfair.)
• roller-coaster lips

If you prefer a more anatomically faithful description then use any of the words below.

The technical term is a tubercle, though given the other meanings of that word it's not very poetic.

A more aesthetically pleasing term is Cupid's Bow.

The term for the border between the skin and the lips is the vermilion border. (Note the spelling; it's one l.) There is a vermilion border of the upper lip and the lower lip.

The vermilion border is the normally sharp demarcation between the lip (red colored) and the adjacent normal skin.

I don't know what a plastic surgeon might call the extra curves (beyond the Cupid's bow) on a lip like the one you pictured. Maybe an undulating vermilion border?

I suggest that the footballer has a pronounced or prominent cupid's bow.

Also known on the internet as duck face.