Thanks for providing the original PDF file. That file plus a download of the font file in question resolves this issue completely.
As can be seen here in Document Properties => Fonts, the CloisterBlack-Light font is not embedded in the PDF file at all:

As such, unless the font is installed on the system viewing the PDF file and the Use local fonts option is enabled, Acrobat does a font substitution, which in this case is Adobe Serif MM leading to the ugly rendition that you see.
I tried installing the CloisterBlack-Light font on my system and reopening Acrobat and the PDF file resulted in the text being properly displayed with this font.
You may then ask, why didn't InDesign embed the font in the PDF file that it generated? Simple! The font has its security flags set to disallow any embedding whatsoever:

Normally, InDesign, Illustrator, and Photoshop all embed fonts as subsets unless the embedding flag prohibits such embedding.
The font might technically be problematic, but the issue here has nothing to do with those other technicalities!!!!
Your solution is to find another font that allows embedding. Note that for fonts that disallow embedding, their licenses oftne also prohibit so-called “outlining” or rasterization. Doing either of these two hacks may be get you into legal trouble unless you can find the license itself, ascertain that thee are no prohibitions or get permission of the font's designer or foundry to do so. (If you find that designer or foundry, maybe you can pursuade them to provide a non-restricted version of that font!) Note that “outlining” or rasterization can seriously degrade output quality both for display and print!!