That throttle link IS important because the piece that is missing contains a screw to spread the two plastic pieces. This synchronizes the carb and timing at idle. And, it breaks frequently. There is a place here on the right coast I believe in Maryland, which would probably have the part, but I can't for the life of me remember the name. Have you tried boats dot net?
The timing plate on almost all 9.9-15 Chrysler and Force engines was the same so if there is a marine junkyard anywhere near you, you could also swap in an older style 15 carb with the all metal links.
Before changing to the metal typ. Try Franzmarine, if someone has this linkage he is the man. He has almost everything for Chrysler/Force OB.
Maybe not cheap but instead of mess with the metal typ and found out it do not fit really good.
From the video, it sounds and looks like the motor is trying to increase in rpm but as soon as it does, it misfires. This is a good indication the timing plate is not advancing with the rpm as required thus misfires. Without load (in neutral) you can actually rev the motor using the throttle link but not if it is loaded. Actually I can do the same with my 125 revving it by moving the throttle bar link and it will rev without having to move the timing. But as soon as you put load on it (in gear) it will die unless you rev it using the timing tower which also advances the timing with increase in rpm.
Not sure one of these is the Maryland source you had in mind, Frank, but either might be able to come up with the part: Fairwinds Marina | (Fairwinds in Annapolis. Ask for Brian.) or American Outboard Motors and Salvage (American Outboards and Salvage on the Eastern Shore – also a good source for decals, btw. Ask for Dora.) Fairwinds was a Chrysler dealer for years, and has a big backstock of used and NOS parts. American Outboards is acres of outboard salvage, and do repairs and detailing – interesting place. But probably best to try Fairwinds first.
Looking at your first post the engine is running in a bucket with water.
But the waterline is to low, you must have the line up to about 2 inches above the partline for the gearcase.
The waterpumphouse is mounted right there and the impeller is not selfsucking it has to be water in the pumphouse when starting.
Try to put the engine in a deeper bucket an se if it starts to pump water.
If this not solve the problem you have to check if the coppertube is correct inlined with the pumphouse.