I believe the author has published it online.
I agree. It is posted at his publisher's website.
However, I am unsure if I'm allowed to read it.
This answer assumes you are in jurisdiction whose copyright laws is based upon the Berne convention (i.e. the civilized world + USA).
Assuming it was the author published it online, it is perfectly legal to read it.
Technically, the author is performing his work by putting it online, and by reading it, you are just enjoying his performance.
Also, if you are in a jurisdiction with an explicit exception from copyright for personal use, or where fair use allows making copies for personal use, it would also be legal to download it, or to print it on paper (but for personal use only).
As for downloading and printing for non-personal use - that is not legal in Berne jurisdictions.