Excellent.
It is in line with the drain pipe.
Doubtful. If it was cut after the slab was poured, it is very unlikely they would cut to a precise 18"x24" measurement for access or a repair. And even if they did, you’d see the continuation of the cuts beyond the edges. I agree with the OP - whatever its purpose, it was there when the slab was poured.
Would you believe an obsessive compulsive repairman?
I’ve worked with a few concrete cutters. And…no. 
The plumber did it with a cold chisel in my experience.
What does a concrete cutter use, an electric saw?
I can’t imagine chiseling through a concrete slab by hand, and certainly not with clean lines like that.
Concrete saws look like this or this with a circular blade. Because of that, the cut at the surface extends beyond the cut at depth, so you’ll always end up with a cross-hatch at the corners.
In this pic http://i44.photobucket.com/albums/f44/JoeyJoeyPP/Mobile%20Uploads/20160804_195218_zpsed8wagoh.jpg
is that a condensation line going into the concrete floor? If so, your basement has a French drain, and if the French drain or other type of drainage/swale system was added, it would be normal to cut through the floor to connect drainage pipes and add material to make the sub-floor drainage work.
That is my point, it would be pretty ugly.
When things like back-flow valves and clean-outs are installed, a box is built around it for access before the slab is poured. Sometimes a plywood lid is also put on ans occa
Damn windows key.
When things like back-flow valves and clean-outs are installed, a box is built around it for access before the slab is poured. Sometimes a plywood lid is also put on and occasionally slab level ends up higher than the lid and you get a rectangular depression in the concrete over the lid. Usually you will see cracks due to shrinking. Knocking on it would produce a hollow sound.
If this is simply a rectangular depression in the concrete with out any cracks or sign of a lid, I would assume it to be an artifact left from a piece of plywood or Styrofoam on the wet slab. Finishers will sometime use a piece of Styrofoam as a knee-board to make minor repairs to a wet slab. Usually they would touch up where the knee-board was with a trowel after they removed it though.
It does not look like a repair or patch to me - those are rarely pretty. I still think the most likely explanation is an access for something mechanical.
New thought, and IMHO, I think it makes sense. First off all, the spot where the hole is doesn’t really make sense for anything to be. It’s under the stairs and basically in the way for just about anything. Also, regarding some kind of knee board, while I understand that, the basement appears to have been finished with some kind of power float. I can see the large arcs where they went back and forth with it (a power or bull float). Also, I can see anything in that area that would require using a hand float when the rest of the basement didn’t.
My thought is that since this hole is right under stairs, perhaps, they formed it out and didn’t concrete that area so that they could set a ladder in there. That way after pouring the concrete, someone could finish it and then have a way of getting out. This would probably mean that the basement slab was poured after they framed out the first floor or, at the very least, poured the walls, but, it’s a thought and does make a bit of sense.
Very quickly doing a Google Image Search, the only picture I could find is of someone setting a ladder on some plywood and using that to get out. That too could work with this theory since, upon closer inspection, there’s some pockmarks in the hole which tells me it may have been part of the same pour, just not floated.
Also, as far as the condensate line, yes, that is one, but I believe the floor drain is part of the sanitary drain system. So far as I’ve been able to tell, there’s one storm drain in the house. It’s connected to the sump pump (far away from all of this) and is stubbed in about 5 feet above the floor). It’s also, I think, connected to my gutters. I haven’t dug into the codes, but I’d be surprised of the floor drains could be connected to the storm drains. At least around here, I believe they drain directly into Lake Michigan.