Kelvin connection, more or less, yes. It's a little more significant than the basic case, because you want low ESL in the sense path, as well as the correct resistance. Taking the sense trace back under the resistor maximizes coupling with the resistor (heh, well, if there were no ground plane inbetween; is this 2 or 4 layers by the way?), potentially canceling out some of its ESL.
The ground connection could be made in the same way, though it may be more important to have a wide, low inductance connection there, and simply tolerate what ESL it gives. It is about as short as can be.
Note that stray inductance is proportional to trace length. There is a geometry factor, of course: a wide trace has ~proportionally lower inductance than a narrow one. Also proportional to height over ground plane, so a 4-layer board with closely spaced inner planes (close to the outer layers, that is) is very superior to a 2-layer board, even a fairly thin (say 0.8mm) one.
The same is true of components, so wide-body resistors and capacitors are preferable over their regular lengthwise variants. Note this isn't a gimme, as resistors are typically trimmed by notching the material with a laser cut; the best current sense resistors are made with multiple cuts, effectively several normal (lengthwise) resistors in parallel on the same chip. (You can do the same yourself, of course, using multiple long-style resistors in parallel.)
Separate grounds are to prevent 'switching ground noise' coupling into the sensitive analog sense areas. Stitching one big ground plane together is quite likely to create all sorts of nightmare artifacts.
I wouldn't be quite so, alarmist about it... The motivation is to keep switching loop currents, and their associated voltage drops, away from the analog control signals. That's all. If you've not put the transistor, diode and cap on that side, there won't be much to worry about. They're just being careful.
There's nothing wrong with putting that switching loop on the ground plane, without cuts, either. You just have to take all the signals (input, output, control, whatever) back through a common path and point, so that the voltage drops cancel out. Add filtering to take care of what's left that doesn't cancel, and you can get quite low EMI levels already, say 40dBuV. Achieving lower, probably requires shields over the switching nodes/loops anyway; which is maybe not
heroic effort, but still a significant step up.
Tim