This happens no matter what Filter mode I am using.
I figured the way to reproduce this problem.
What I am doing in my project is:
Change the Size attribute of the Camera component from 5 to 10
Change the Scale Transform for my Spine object from 1 to 0.3
In Game view, increase the value of the Scale - more I zoom, more pixelated the object will be.
But actually you can just switch the Camera size to much higher values like 30 and zoom in the Game view.