There is quite a bit of confusing information around about use of steel shot. The video mentions that high performance steel shot loadings should only be used in guns with fleur-de-lis proofing. While this may be a good general guide it is not absolute. When researching whether I could use steel shot loadings in my 1984 Miroku O/U Sporter gun which has Invector chokes but no steel proofing marks, I came across the following information on the Miroku/Browning site;

"All hunting or sporting shotguns (over-and-under or semi-auto guns) by Browning, Winchester and Miroku fitted with the original chokes (Invector, Steel Invector Plus, Stainless steel Invector Plus, Teague, Briley, Midas, Diamond, Signature chokes) can fire "high performance" steel shot cartridges.
Tested at the Ličge test bench (high performance 1370 bars) in accordance with European law on the use of steel shot."

Converting 1370 bar gives us a pressure of 19870psi which is certainly a step up in pressures for a shotgun. There is a misconception that steel shot will score the bore of shotguns not made for steel however the bore cannot be scored if the steel shot is not touching it. Wads for steel shot are thicker and longer so the shot is fully contained in the thick plastic cup, a warning made in reloading information for steel shot is to absolutely ensure the shot is fully contained in the petals of the wad, unlike heavy loads of lead where often even in factory loads, some lead shot sit above the petals and contact the bore on the passage through.

The issue with steel shot is the choking of shotguns where hard steel shot does not compress to the same extent as lead shot hence more open chokes or stronger thicker walled, stainless steel, etc., screw in chokes are needed to prevent muzzle bulging and peening of choke threads.