Finally, got confused. Decided to write to Derek Leinweber directly to get precisions. Obviously watching 2 differents videos is not the best way to learn. Dho! Here its answer:
The quarks and electrons do get their mass from the Higgs field, but the small mass of the three quarks composing the proton contrasts the mass of the proton by two orders of magnitude. The mass of the proton comes from the gluon field.
So, now you know.
Tell it to your friends!