First off my old drafting teacher would go on a small rampage about that drawing for the head "Arbutus", it appears saving paper was important by the maker.
Anyway numbers 132, 136, 137, are spacers, 127 is the spindle, 142 is the quill, 131, 135, 138 are the bearings for the spindle, all inside the quill. The adjusting nut 129 sits on top of 130 , the locking washer. 133 and or 134 are the bottom retainers and appear to be held in place by pin /screw 139.
There is a possablity the whole quill/spindle assembly will come out the bottom of the head with removal of down feed and quill lock and pin/screw 139. A big maybe!
If the play/movement is between the spindle and the quill, a number of things could be the problem. Lack of preload on bearings -- nut 129 not tightened enough. Anyone or more of the 3 bearings with wear or packing it in. Pin/screw 139 missing,worn,loose, allowing 133/134 to move down, and wear the quill body.
If you have 2 dial indicators, mount both on the head, extend the quill and lock it, put one on the quill, put the other to the spindle, see which is moving. If all good there, move the quill one to the collet/toolholder, see if anything moves. May have to remove that nose piece, 133/134 to get on the spindle, appears not by picture. Appears spindle maybe a morse/? taper and an adaptor up sizing to spindle size.
As per" thestelster" and others, check the draw bar and any adaptors being used. A new adaptor may have a longer nose not allowing draw bar to tighten proper, a few washers could be an easy temp. fix. You should be able to get an idea of draw bar length of threads by putting collet/taper into spindle, lowering quill down to a piece of wood to hold collet/taper in place, lower draw bar into spindle, on to top of collet/taper, measure top of spindle to shoulder of draw bar, remove draw bar and measure thread length verses length from spindle to draw bar shoulder. A few times have found a new to mill tool being a different length and not pulling in proper, to say nothing of messed up threads.
Please note, I am going by pictures and drawings shown,( can't see the vid.) any of my above maybe wrong, not wrong yet today as it's still before noon.