Do gravitons interact with each other?

I'm pretty sure that you are right and Wikipedia is wrong. In the linearized gravity approximation at weak curvature, you ignore the gravitational self-back-reaction, but in general gravitons carry energy (as evidenced by the work done by gravitational waves on the LIGO detectors) and therefore contribute to the stress-energy tensor of general relativity, therefore sourcing more gravitons. Also, some quick Googling finds lots of references to multiple-graviton vertices in effective quantum gravity field theories, whereas the Wikipedia article paragraph you quote has no references.

The issue of how gravitons can "escape" from a black hole without needing to travel faster than light is discussed at How does gravity escape a black hole?. The short answer is that gravitons can't escape from a black hole, but that's okay because they only carry information about gravitational radiation (which also can't escape from inside a black hole), not about static gravitational fields.

So in quantum field theory, the gluon is an operator which changes the color charge of a field. Since the gluon field itself carries color charge, the gluon-gluon interaction has the same strength as the gluon-quark interaction. Furthermore, since the QCD coupling constant is $\alpha_S \approx 0.1$, Feynman diagrams with virtual QCD particles in loops contribute with roughly the same strength as one-gluon exchange. The inability to ignore higher-order corrections is why we call QCD a "non-perturbative" theory.

By contrast, the photon couples to electric charge, but is itself electrically neutral. Photon-photon vertices therefore don't appear in the Feynman diagrams that describe electromagnetism. However, photons can interact with virtual particle loops: each photon spends some fraction of its time as a virtual electron-positron pair, and other photons can interact with those virtual charged particles. This is negligible because the electromagnetic coupling constant, $\alpha_\text{EM} \approx 1/137$, is about ten times feebler than for the strong interaction. So we can describe electromagnetism quite well, especially at low energy densities, by considering only one-photon exchange between charged particles and ignoring loop corrections, including photon-photon scattering.

Since the gravitational force between the charged fundamental particles is $\sim 10^{40}$ times weaker than the electric force, any perturbation-theoretical approach to gravity will have totally negligible interactions between gravitons, for the same reason that electromagnetism allows you to neglect interactions between photons. I don't think they're impossible, which seems to be the statement that's bothering you; but I think that they're negligible.