gluons wouldn't make much sense in the range of the nucleus... the strong force is effectively mediated then by Yukawa interactions (mediated by a scalar particle, such as the pion). It's called residual strong force. I guess that's what the picture you sent wants to show.
I grant you that the WIki animation goes a little fast. But if you read the lemma (and a bit of the adjacent ones) a lot becomes clearer and maybe then there remain one or two more specific questions ?
Gluons are the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles. The gluon can be considered to be the fundamental exchange particle underlying the strong interaction between protons and neutrons in a nucleus. That short-range nucleon-nucleon interaction can be considered to be a residual color force extending outside the boundary of the proton or neutron. That strong interaction was modeled by Yukawa as involving an exchange of pions, and indeed the pion range calculation was helpful in developing our understanding of the strong force.