If you have a phone that's old, slow, poor battery, having issues, doesn't have Bluetooth 4+, bad antenna placement, extra, then the dongle could make a big difference.
If it turns out the toy is having issues, being able to point to it not working with both your phone and computer, then it's easier to prove your case and get it replaced. That is assuming it's still under warranty.
Another way of testing, see if one of your friends will let you test with their recent up to date smartphone.
Some people prefer running it on their computer. Because it frees up their phone for other stuff.
FYI, Human bodies can easily block RF signals. The gen 2 toys, have better signal then the gen 1 toys.