I believe that the half-moon chainguard is a minimalist design that shields only the portion of the big ring where a rider's pants leg would fall down upon and snag the teeth. That shows a thinking tinkerer for sure.

Generally, half-steps up to the big ring have at least as much to do with shifting performance (up to and down from the middle ring in the case of a triple) as they have to do with gearing preference. Old-style plain chinrings don't lift and drop the chain aggressively unless some degree of half-step-plus-granny is used for the sprocket selection.

I've seen quads before, but those added the 4th ring to the inner side instead of like this one.

One thing to note is that current gearing hardware could have us trending toward a narrow 4-ring crankset!
Firstly with 11-speed chains, and secondly with the arrival of the electric indexed front derailer.
Additionally, as a "racing quad" with only modest 7 or 8-tooth jumps between sprockets, the sprocket spacing can be narrowed toward what is used on rear cassettes, much narrower than typical chainring spacing. Thus a modern quad could be no wider than a 9-speed triple.

And, with electronic coordination of the front and rear shifting, one could realize a very large number of closely-spaced gears, with near-perfect chainline maintained continuously and automatically for a real increase in efficiency.

As for the added weight of a close-ratio quad, witness the one-piece CNC cassettes which have adjacent sprockets fully supporting one another, for structural efficiency i.e. high-performance design.