This doesnt seem to be doing gamma correction, but something else instead. The image just appears brighter and more saturated.
If I set the HDRI gamma to 1.0, then use shift+e > gamma 2.2 to preview what it should look like, it looks correct.
I can also resave the image as openEXR in photoshop and xnview displays it correctly. So it seems there is a bug in the gamma preference for HDRI. The same problem occurs in xnview MP too.
Here is the test image used in my screenshots (Im using the 4k version)
https://hdrihaven.com/hdri/?h=san_giuseppe_bridge