Yes, you have a lot of play there. There's an awful lot of wear on your bushings which is causing that side-to-side play you demonstrated second, there should be pretty much no play in that direction and it'll definitely be affecting the ignition timing. Those bushes are going to need to be replaced.
If it was me, I'd change those bushings as a first step then see what it looks like as that might take up a fair bit of the end float too. The end float is less of a worry until it gets to the point where the auto-advance can foul the back of the contact breaker backing plate (which yours almost certainly can).
Yes, the shims are fitting in the recess on the end of the housing which fits in the timing chest, on the right hand side of the bike, under the cog (pinion is a fancy term for the smaller of two meshed gears).
You don't actually need to remove those three screws to do all of this, the bushes can be drifted out and new ones fitted with the aluminium distributor housing on the bike. I took it off because a) it's easier to do on the bench and b) It's easier to show it on a video.
For the benefit those at the back of the room
. When you get new bronze bushings, they are often made very slightly thicker than you want them. Fitting them in the housing isn't usually too much of an issue because -as mentioned above- aluminium expands quite a lot when heated, so if you heat up the housing, a tight fitting bush will usually press in quite easily.
The inside diameter needs a little more fiddling. It's often slightly undersize AND it can contract a little as it's pushed into the housing meaning it's too tight for the shaft to fit inside and/or move freely. There are a few ways of sorting this out. (in order of "correctness").
1) Ream it out with a correctly sized reaming tool in a pillar drill or (preferrably) a mill.
2) Hone the inside with a small brake caliper honing tool.
3) (what I do) Hone the inside with an improvised flap-wheel made using a piece of aluminium tube with a slot cut in the end and a piece of emery tape or folded wet and dry paper stuck in the slot so it's liong enough to rub on the insides of the bushing when inserted. Put it in an electric drill and wizz it in the bushing a little at a time until the shaft is a good fit. So it slides in and out and rotates easily but has no real sideways play.
Remember to clean off any abrasive residues thoroughly afterwards.