In the following sentence:
"The player must not use any artificial device for the purpose of gauging or measuring distance or conditions that might affect his play"
does "that might affect his play" relate only to "conditions" or also to distance? and why?
I pondered over this for quite a while before I decided that "that might affect his play" corresponds only to "conditions". The words "that might affect his play" are an adj clause, as you point out, but they are also a restrictive clause. That means you have to use it to describe "conditions". Another example would be "who lives here" in "the girl who lives here" (note: no comma after the relative pronoun; "who" is this example; "that" in yours). My point is this:
If you extend the restrictive clause to "distance" then the player is permitted to use any artificial device for the purpose of gauging or measuring distance that do not affect his play. Can you see the logic? I hope that makes sense.
Further to the last post: If on the other hand, you are trying to write unambigious rules, then I would go for a re-wording.