They do need exercise to strengthen their muscles, but humans are designed to shed unused muscle way more readily than either tigers or chimpanzees. They need their strength to navigate their habitats and obtain future meals, while we're endurance predators capable of walking our prey to death even while emaciated. Excess muscle on a human is a waste of energy, so our bodies will happily scrap it all for free protein.

Any responsible animal-keeper will furnish the habitat with enrichment structures/items that will provide all the exercise their wards require. Poorly-kept animals (or especially lazy ones) will lose muscle tone and put on fat.