What physically makes chainrings have a specific speed compatibility? Chainrings are sold as having a specific compatibility for only certain speed setups, some overlapping across many. What physically makes this the case?

From what I understand, 5/6/7/8/9 speed chains all have the same internal width, 3/32", and the only difference is the external width of the chain. Does this also extend through 10/11 speeds as well, or do they have smaller internal widths which would necessitate skinnier chain rings as well? Or is it the case that the external width just keeps shrinking?

IF the difference is only the external width, then it would seem the only compatibility issues would not be in the chainrings themselves, but the spacing in between each one. If it was too small/too wide a chain, the chain would hit the next chainring, and if it was significantly too large the chain may fall in between rings. 

However, it would seem that you could use the same rings with a wider chain (9 speed rings with a 5/6/7/8 speed chain) if you put appropriate spacers between the rings, such as these. The opposite may be possible if you're willing to grid / mill the appropriate amount off the mounting pad.

What this would also imply is that with the right width spacers (and bolts that can accomodate them) you could always go down speeds with a given set of chainrings.

If that is not the case (say 11 speeds have a different internal width), then they might be too wide for the chain an you'd have to remove material near the teeth to make them fit inside the chain or conversely that you'd be wearing on less of the chain than you should so your chain wouldn't last as long.

Furthermore, some rings are marketed as 5/6/7/8 speed only, some 9 speed only, and some 5/6/7/8/9 compatible. Is this some sort of blending of the two specifications (the spacing being some compromise between true 8/9 speeds) or just that they're made for one but tested to work on the other (or just a marketing trick)?
The internal width is obviously one important feature.  But for indexed shifting the ring has a pattern embossed on the side facing the smaller ring that catches the pins of the chain when shifting.  The combo of the embossing depth/pattern and the ring-to-ring spacing affects what width chain (and brand chain) will work best with the ring.

I've no idea what combos can be expected to work with what, though.  I lost track when they went to 8 speeds, and now it's a total free-for-all.