The filament choke is hidden under the piece of polycarbonate. Much larger gauge wire. The burnt choke is in that filament circuit as well .
I have seen many videos of TL922's with all kinds of issues, but that choke did not appear to be discolored in any of them. Curious.
The owner doesn't know how to tune an amp any more than the man in the moon, and I think he was driving it with a TS950SDX at probably 150 watts . Even after he had lost one tube.
So, who knows.
This is what I originally thought. The choke that is burnt up in the pix, is the extra (single winding) choke that's used for the B- return. ( It's wired between the junction of the series cathodes...then back to the bias, cutoff bias, then to CT of fil xfmr). The reason it burns up is simple. With either the filament gone open in either tube, OR either tube is UN-plugged, the remaining good tube will still light up. With 10 vac across the entire secondary winding, their is still 5 vac between the CT and each outer end of fil xfmr sec. You end up with 5 vac across the good tube.... BUT the return for one side of the good tube's cathode is now through that single winding choke...... which is obviously not rated to handle 15 amps CCS. (that single winding choke that got zorched only has to handle cathode current, which is the sum of dc plate current + dc grid current, so maybe 800 ma + 300ma = 1100 ma).
That single winding choke being zorched, happens a LOT more than you think. Hams have a problem with what they think is a grid to fil short on one of the tubes, so UN-plug one tube at a time to isolate the bad tube. With one tube UN plugged, blamo, there goes the single winding choke.