The main reason that you need to use Stripe for this app to work is Stripe's ability to handle subscription 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 3rd party app, like this.
Stripe is a FANTASTIC service that you'll love once you start using it. If you don't already have a Stripe account you can literally get one set up and start accept credit card payments in less than 5 minutes. Here's more details on that: https://stripe.com
Another Side bonus of the fact that the app uses Stripe is that there no need to change anything with your current payment gateway. When someone makes a donation it doesn't go through the regular shopping cart and checkout process so nothing needs to change there.