When it's time for games of tug-o-war, the pups in our pack love woven nylon straps. We choose these straps for toys for the same reason adventure equipment companies build their backpacks and climbing harnesses around 'em – they're light, strong, and long-lived. Woven nylon is resistant to abrasion and also has excellent tensile strength – that's how strong a material is when it's under tension, like during a tug game – but isn't indestructible.
If you know your dog likes to shred nylon straps apart instead of tugging, you can always cut the strap portion off of the larger toy and dispose. Toys with straps in Super Chewer boxes are always intended for active play, not idle chewing, so your dog needs a human involved. It takes two to play tug-of-war, after all.