I wonder if the inductor is part of a clever dance to turn off the SCRs, rather than a PUT protection device. Consider that the circuit is in the first phase (red diagram in the video), and we want to turn the SCRs off and switch into the second phase (green diagram in the video).
1. Now, we turn on the bottom right IGBTs. This is not shoot-through, purely because the inductor is there -- it keeps the current steady, and allows the IGBT to succeed at pulling the Sternum point to ground.
2. With Sternum at ground, the Apex will fall to ground, and with zero voltage across them, the bottom left SCRs will turn off. Victory #1.
3. Now we turn the IGBTs back off. With the bottom left SCRs now off, there's nowhere for the inductor current to go, inductor current collapses to zero, and the top SCRs current consequently drops to zero and they will also turn off. Victory #2.
4. Now we trigger the IXYS and turn the IGBTs back on, and we've successfully transitioned into Phase 2 (green).
The only missing piece I see in my story is the inductive voltage spike that the inductor would produce in step 3, but maybe there's some sort of clamp/snubber/flyback diode somewhere.