Short answer, yes. While running, your feet go through a simple motion called the running gait, landing on your heel, rolling your foot from heel to toe and finally, toe-off.
When you step on your foot running, you exercise a force between one and a half and three times your body weight. Running shoes have mainly two functions. One, absorb part of the shock, this is called cushioning, and two, guide or encourage your feet to move in a safe and efficient manner through the running gait.
These shoes are designed and optimised for this simple motion. Other sports have different movements, sudden change in speed and direction, stops, jumps, rotations.
When you bring the shoe that was designed for other sports, you are not getting the benefits a running shoe is meant to give, and you’re potentially putting yourself at greater risk of injury.