What are these markings on a Shimano FC-M770 crank?

The only people that can answer this with 100% genuine authority would be Shimano's R&D team.

Clearly those marking are not there by chance so lets presume what is a reasonable reason :

1. Weight Saving (it's going to be a fraction of a gram at best) but some people are picky
2. Reduced Drag (it could be a fractional difference while spinning at 90rpm as opposed to 70rpm)
3. Intentionally built in to make them harder to clone in the manufacturing process

Your best bet is to get in touch with Shimano and ask them, they will either tell you or they wont.

I'm guessing, but these grooves could be a cunning way of reducing pedal cross-threading.

When you fit a pedal axle into the crank, it has to be at right angles to the ground and to the centerline of the bike. There are few visual clues on the bike, with most tubes being at some angle.

The cranks themselves have a subtle curve to them as well, so your "eye-cromiter" can be deceived resulting in mangled crank threads.

By having some clear lines, it helps the pedal axle to be threaded in orthogonally to those lines, saving on warranty claims and bike-downtime.