While not completely identical, it looks very similar (I also only have strong protanomaly, not complete protanopia, so I wouldn't expect it to look identical).

Color-vision deficiency simulations collapse colors along the confusion lines, but this can be done multiple ways. These different mapping will all look the same (and identical to the original) to a dichromat but will appear different, with different perceptual differences between colors, to a color-normal individual. Simulating in a way that accurately portrays perceived color distances is still an open research problem.