No, the one you linked to is for 0.404" pitch chain. It may work, but the top plate guides will not be in the same position as they are on the ones made for 3/8" pitch chain.
I was in the same dilemma. I bought four of the Pferd ones. One for the 3/8" LP, 3/8", 0.325" and 0.404" pitch. The 3/8 pitch one comes with 13/64" files. The 0.404" pitch one comes with the 7/32" files, which is what you linked to above.
Pferd 17300: Pferd CS-X™ Chain Sharp Precision Filing Guide 5/32" (4.0mm) for 3/8LP Chain
Pferd 17301: Pferd CS-X™ Chain Sharp Precision Filing Guide - 3/16" (4.8mm) for .325 Chain
Pferd 17303: Pferd CS-X™ Chain Sharp Precision Filing Guide -13/64" (5.16 mm) for 3/8 Chain
Pferd 17304: Pferd CS-X™ Chain Sharp Precision Filing Guide -7/32" (5.5 mm) for .404 Chain
I bought the 17303 and swapped out the 13/64" files for the slightly larger 7/32" files I already had. Like you said, it wasn't as easy as it sounds.
Here they are on Pferd's website:
https://www.pferd.com/us-en/product...r/1-8-chain-sharp-csx-w-round-and-flat-files/