They didn’t request a T/O clearance.
They reported ready reaching the runway.

I plotted it from the dimensions in FAA Order 6750.16, "Siting Criteria for Instrument Landing Systems". There are no markings on that side of 18L because there is no ILS critical area there, the LOC critical area begins shortly after the 1000ft markers on 18L, the G/S critical area is on the other side of the runway and does not extend to the runway itself. There was no way the SWA could have taken off without violating the required separation and the LOC critical area on the T/O roll.

I'm not sure about the 737, the Boeing I fly requires a 30 second runup in those conditions. If that's the case with SWA, that was poor SA from them to accept the clearance and not mention it to tower.
Still, nothing explains why the tower wants to run the operation that tight when conditions are so low (on the second approach, RVR was 800 at TDZ).

Certainly line up would bust the glideslope critical area which is demarked on the other side and is arguably more critical than the loc.

Regardless of the reason for the runup, under certain circumstances, it's required. But yes, it is to remove ice, as well as to heat the nacelles. The point was (is) that there are very valid reasons to do a runup ON the runway, despite an idiotic dismissal to the contrary. It's quite possibly irrelevant here, as it didn't enter into the recorded dialogue, but was merely introduced by another poster.

In a Boeing , one rejects a takeoff, and aborts an engine start.

That's what I thought too but rather surprisingly, the G/S critical area does not always extend to the runway itself. Makes sense given that autoland does not follow GS after a certain point.

You know I can see this. The gs antenna is off to the side of the runway. The critical area is only on the side where the gs is. Interesting…..

Just a statement of fact here. I’ve seen a lot comments about the possibility that SWA may have just switched over from ground and might not have known about FDX. That’s not true. In the takeoff clearance, the TWR Controller advised FDX was on a three mile final. Simple math tells you that’s about 90 seconds from touchdown at 120 knots. You could make the argument they were distracted or go-oriented, but not that they were not informed.

So they would have missed a “nonstandard” call from TWR also?

My simple math says that the FedEx flight had better not have been flying the procedure at 120 knots, and also that a report of a "three mile final" doesn't necessarily mean the airplane is at 3.0 DME...it may be much closer. Certainly, however, SWA was informed of the traffic. Perhaps the tower controller thought SWA would be off a bit faster, given that their taxi speed is about five knots less than Vr.

3.0 DME to 18L is a 1.4 mile final.