To replicate:
1. Have a damaged bow in your inventory, 1 piece of Redstone and 7 pieces of cobblestone.
2. Use a crafting table, make sure your recipe book is open, filter by "showing craftable".
3. In theory, the dispenser should show up as craftable, since you have the materials required. In this case, it does not. Probably due to the recipe not recognizing that a damaged bow is allowed.