I don't believe the OP was all that far off. The routine called for either backward sprint w/sled or Prowler. Not having access to either during his workout, he asked if backward sprints without resistance would be a good substitution.
This program has its challenges in a small and/or commercial gym. The amount of equipment I need to tie up is more than I like, particularly for the deadlift complex (3-4 barbells + power rack).
As for exercise substitution, I look at the load type (e.g., Overload, Strength, Strength-Speed, Speed-Strength, etc.) and attempt to come up with something useable in my gym that fits the bill. I believe this was CT's intention--to teach people the program as opposed to hand holding them by prescribing exact exercises--but, I digress.
The Prowler exercises fall under work capacity. I took this and decided, in the absence of a prowler/sled, I would perform farmer walks with dumbbells. They may not necessarily target the exact muscles as those CT discusses, but I believe farmer walks are consistent with the overall objective of work capacity. This may or may not work for the OP (depending on the size of the gym). I would make sure to follow the loading parameters for this load type (Max weight you can move fast for 30 meters).