There are two different notations dealing with two different issues. Any time you need ATC radar to enter the approach, they put the big RADAR REQUIRED in the planform view. If you need something other than the systems listed in the title in order to fly the approach, they list that system as "required" in the notes system.
In this case, clearly, you cannot enter the approach without ATC radar (no feeder or transition route from an airway fix and it doesn't start at a navaid), so they put the big RADAR REQUIRED on the planform view.
However, the "DME or Radar required" in the notes is a little more complicated. While it is true that once you get onto the approach, you can fly the full ILS all the way to either the primary or alternate missed approach holds with neither ATC radar nor DME, you must have either DME or Radar to fly the LOC-only version in order to identify the FAF and stepdown fixes. Obviously, they can't make this an "ILS or LOC/DME" approach, since you can use an ATC radar fix instead of DME on the LOC portion, and if they put the "/DME" in the title, you wouldn't be allowed to fly the LOC approach without DME.
Put it all together, and I think what happened is they put in the "DME or Radar required" note even though DME is not required for any version of the ILS because you must have one or the other for the LOC approach, and you always have to have Radar for even the ILS. OTOH, for the LOC, if you don't have DME, ATC must call the FAF and stepdown fixes to you. As a result, the "DME or Radar required" does not add any requirement to the ILS which isn't there already (if radar is required for everyone, you've got that already), but it does remind the LOC flyers of the need for either DME or to get ATC to call the fixes.