`python3` is the standard executable name on Unix-like systems, in accordance with [PEP 394](https://www.python.org/dev/peps/pep-0394/). The shebang is just part of the script (verbatim) and isn't meant to be special in the case of the Chocolatey package; instead it relies on `PATHEXT` to be executable (see https://docs.python.org/3/using/windows.html). It just so happens that git bash is MinGW and sees the shebang as special. (That you need to type `googler.py` instead of just `googler` to get to this "sort of works" situation is further proof that it's not intended to work at all.)
Does it work if you change the shebang to `#!/usr/bin/env python` in `/c/ProgramData/chocolatey/lib/googler/tools/googler/googler.py`? It will require manually editing the script every time you upgrade, which apparently isn't ideal, but I'm afraid I don't want to change package `googler.py` since it will make [VERIFICATION.txt](https://github.com/zmwangx/chocolatey-googler/blob/master/legal/VERIFICATION.txt) that much more complicated.
Alternatively, maybe you can create a `python3` symlink for `/c/Python37/python` and put it on your `PATH`. (I can elaborate if you don't know how to do it.)
Still, I recommend **using Chocolatey-installed googler in its supported environment, i.e., cmd or PowerShell.** To **properly install googler in a MinGW environment**, you probably want to follow this instead: https://github.com/jarun/googler#downloading-a-single-file.