The piece your asking is is a piece of copper which is threaded into the canvas wick. the bottom part of the wick is ok. That end of the wick is supposed to be loose whick looks like it makes "L" while looking from to the top. The other end is wedged and twisted locked into place by the copper strand.
How are cats to learn pressure stove operation if you run them off? The bit of fiberglass braid is a sort of priming fuel sponge. On mine, it is held neatly and snug under the burner bell, brass wired to the U shaped burner bell pivot. Also, dragonfly pump is not compatible/interchangeable w/ other MSR stove pumps. Dragonfly stove MUST have its own particular pump. Whitegas is low octane, maybe 50, by memory. Volatility is sky high :D
You're not letting it prime enough before turning on the gas. The priming fuel needs to burn almost all the way before you turn the gas on. and the cap needs to be seated a little better. Good stoves though. The Dragon fly is a much better stove . The XGK is awesome but built for melting snow in high altitudes and the Dragon Fly is better fro cooking in all conditions.
Also when performing your tests, You really should put that supplied aluminum heat shield underneath the stoves so as to not catch the wooded table on fire.
In future I'd suggest actually reviewing equipment you know at least something about and have used before. This made for painful watching... at least until I stopped the video 5 mins in.