The Vout and Iout equations will be quadratic in form as shown in EQ 8. For figure 7, I calculate Vout = [12 +/- SQRT(12^2 - 4 x 4ohm x 5W)] / 2 = [12 +/- 8] / 2 = 10V or 2V. Vout = 2V is the correct answer so Iout = Vout / Rload = 2 / 4 = 0.5A.
I did find a similar waveform in the TPS2590 datasheet (TPS2590 uses a similar power limiting engine) which does show 500mA for the 4 ohm load start up waveform (Figure 7 coincidentally of SLUS960F).
As far as TPS2421-1 datasheet, figure 19 I do not know how the "short" condition was applied to the hardware and as such cannot comment on how accurate the current waveform is. But, for Rload approaching zero ohms the current should approach ~Plimit / Vin = 5W / 12V = 417mA. So, the figure current scale appears to be in error.
For your case, I would expect Vout = ~1.4V for the 3 ohm load.