I would like to run this speedrun, but I only have the digital deluxe version.

In this case, can I use the digital deluxe version?

The Digital Deluxe Edition is, in short, a set of multiple DLC, I think you should choose whichever of these two you prefer.

Case1 "By not using DLC items (100,000 gems, shoes, etc.), the speedrun will be treated as no DLC."

Case2 "Make this a Speedrun that uses DLC (the DLC usage category will not be created unless you run Speedrun)"