It shows up in the NE5532's weaker output stage that TI puts the "lipstick on a pig" by deleting any such revealing specs. 600 ohm drive is a basic requirement in pro-audio for many decades.
It is still technically specced into 600ohms, but they have removed the Vop-p spec into 600 ohms.
How the op-amp is actually doing at that heavy load - you need to know if it's crapping out.
Reduced output stage capabilities - what a snake must then do is scrub that, hide the graphs, delete the numbers:
"Removed Maximum peak-to-peak output voltage swing, Small-signal differential-voltage amplification, Maximum output-swing bandwidth, Output impedance, Crosstalk attenuation" - all deleted!
The TI 2015 datasheet had 'em. Why not update the datasheet to modern standards that include THD etc. at load? Unless you're hiding stuff.
Legacy part's spec: 10V
RMS drive into 600Ω, 100kHz power bandwidth at load V
OUT=±14V R
L=600Ω V
CC=±18V
A long time ago, alternate NE5532's met this original claim (National Semi listed the LM833 as their "drop in replacement" for the NE5532, despite it only being rated for 2kΩ loads).
I expect the part to meet or exceed the original's performance instead of laundering the old part's datasheet.
Your old spec table seems to be for the NE5534 as it gives two comp cap values 0pF, 22pF yet the NE5532 has no comp pins. TI datasheets are full of mistakes.