When a Vault is destroyed, a "Vault protection pylon" appears and starts to spawn enemies. It decays and triggers an explosion if it reaches zero.

According to the research option "Interplanetary Construction 1" I should capture it. The Factoriopedia entry for the pylon says it "can be hacked with Vault security key" to create "Interplanetary warp pylon".

But how do I do that? In this mod "hacking" is normally done by shooting a Vault access key into a Vault access console, and the Vault security key has the Vault protection pylon as a possible target filter. I tried shooting the protection pylon with a sec key in a submachine gun, but that didn't do anything. I tried surrounding it with sec key Gun turrets that have the protection pylon as a priority target, but to no avail: https://fb.hash.works/9yc7KYlE/

What am I missing?

What you need to capture is not the exposed vault core, but the vault protection pylons spawned by vault support requesters. Check factoriopedia entry for the vault access console to see the spawn probabilities.