The main reason you need to use Stripe for Donations Manager is its ability to handle subscriptions and recurring payments. Most merchant accounts either don't have a recurring payment option or if they do it's a manual process and can't be done through a third party app, like Donations Manager.
If you don't already have a Stripe account, you can set one up and start accepting credit card payments in less than five minutes. Visit Stripe for more details.
There is no need to change anything with your current payment gateway. When someone makes a donation, it goes through a separate checkout independent from the regular shopping cart and checkout process.