After listening to the audio a few more times, a couple of additional observations:
1. ATC doesn’t query SWA status until a full minute after issuing takeoff clearance, which was coincident with calling FDX on a 3 mile final. At the status query, FDX would have been within 1/2 mile of the runway threshold. This query also seems to confirm that the local controller has no visual contact on SWA and had no other surface detection capability such as ASDE that could establish the SWA position/status.
2. I think it likely that the local controller thought that the “southwest abort” call was from SWA and indicated a RTO. The subsequent “you can turn right when able” is much more typical of an instruction to an aircraft on landing rollout or RTO rollout. If the instruction was intended for SWA after takeoff, it would have been inappropriately vague and made no sense given that SWA was to fly 170 after departure.