No, the inner notches are less mechanical leverage, less anti-skate. The owner’s manual is right about that. This method is the same as my Origin Live Conqueror, only the attachment points and adjustments differ but it is the same basic design. It is hard to tell without seeing the weight to know how heavy it is but the whole thing looks like it can’t possibly have enough leverage unless the weight is pretty heavy. Which indeed seems to be the case, not enough anti-skate.
First, no worries you haven’t and won’t harm anything. Second, the test for anti-skate is listening and test tracks and it passes flying colors so that is another reason to know there is nothing to worry about. Finally, you are new to LP so in time will learn this, but some records are not perfectly flat all the way to the edge. Look real close you will see some are kind of thick at the edge then dip down before going flat. I think all that is happening is you have a couple of those, when the stylus comes down on that it hits a flat spot starts skating downhill as it were towards the center gains speed and maybe sometimes skips a bit at the beginning before settling down and all is well. I have one or two of these myself. Next time it happens, cue it back up, line it up to drop right where the music starts instead of the lead-in groove, lower carefully, then see what happens. I bet it plays just fine.
So I’m calling it good enough already and our assignment is to see if there is room to make it even better. Simple project, take one or two appropriately sized metal washers and slide the string through so one sits on top of your counterweight. Wala, you now have more anti-skate force! See if that helps. If you want more simply add another washer. If this works then look for prettier washers. If you even can see it. Looks to me like it will be pretty well hidden. Anyway, there you go, problem solved.
As to why, anti-skate is one of the less critical aspects of setup. Some really expensive tables like VPI use an even hokier and more lame setup if you can imagine that, and almost completely unadjustable as well. To top it all off, it uses the twisting torque of the phono leads. Hard to imagine a dumber method and people do sometimes have problems but that hasn’t slowed them down any, still one of the biggest most respected names around. If VPI don’t sweat it and I don’t sweat it probably you don’t need to either.