> The ETC pumps electrons across the inner mitochondrial membrane from the matrix to the intermembrane space to create the proton gradient.

This absolutely does not happen.

Electrons are transported from complex to complex arranged as a chain hence why it is called the ElectronTransport Chain. And indeed this is how it is illustrated in both the 1st two diagrams of your link, where the "path" of the electron(s) is between complexes within the membrane and not in to the intermembrane space. You'll note in the 2nd diagram that at the end the "free" electrons are passed from complex IV to Oxygen in the matrix because oxygen is the final acceptor of electrons in the ETC. This is where the electrons end up, not in the intermembrane space. Free electrons are not accumulated in the intermembrane space (I'm not even sure physics allows free electrons to accumulate outside of some exceptionally rarefied circumstances)

The oxidisation of free FADH and NADH provides high energy electrons at the start of the chain, as the electrons transition between complexes they lose energy and this free energy is "used" to move the H+ ions in "solution" within the matrix to the intermembrane space. That is, the ETC complexes pump protons across the inner mitochondrial member to the intermembrane space. This establishes a concentration gradient as H+ ions are highly concentrated in the intermembrane space.

Also the whole system wouldn't work if the intermembrane space was filled with free electrons while complexes I - IV were "pumping" H+ ions there. If that were the case the H+ ions would immediately neutralise and become hydrogen atoms. ATP Synthase works because it can make use of the concentration gradient between "free" H+ ions in the intermembrane space and the lack of "free" H+ ion in the mitochondrial matrix.