The references to Chapel House Farm on the web site are all (I think) relating to Chapel House Farm on Brick Bridge Road, near the junction of the Peak Forest and Macclesfield Canal.
You have mentioned Compstall in your post title and at first I thought you must be confused by the info that you had, as the above is not in Compstall. However, a quick Internet search reveals that there is a house on School Lane Compstall called Chapel Farm House.
So I think the first step is to try and clarify which of these it is - hopefully from the info that you have.
We have a gentleman called Ray who uses the forum who knows a lot about Chapel House Farm Marple, but I don't know if his knowledge stretches to Compstall or not - I look forward to finding out what he and other locals may be able to tell you.