No, a non-participating royalty interest typically means that mineral interest shares in only royalties, and didn’t “participate”, or receive a share, of an bonus payments that were made under the lease. A non-participating royalty interest often doesn’t include any executive rights, which is the power to negotiate a lease. If that’s true in your case, you are bound by the terms the holder of the executive rights related to your mineral interest agreed to.
If there are any restrictions on post production cost deductions from royalty they would have been included in the original lease agreement. If you only have a ratification and haven’t seen the actual lease you could get a copy of it from the La Salle County deed records. If it is an old lease the odds are probably low that it includes any limitations on cost deductions but since you say Chesapeake, for some reason, hadn’t deducted any for 12 years it would be worth finding out what the lease shows.