It's hard to tell how big that box is in the images - it looks like a "typical" door bell ringer box... but the plate it attaches to looks like it's the size of a typical single gang box. If it covers the dual gang box, you might be able to mount it to your wall with some drywall anchors instead of mounting to the plate?

But, if not, I'd just get a new chime box. Like one of these:

https://www.amazon.com/Newhouse-Hardware-CHM1-Chime-White/dp/B019BW9TX6/ref=sr_1_4

Should cover a double gang sized box (with a cover plate over it). Put a couple self-drilling drywall anchors in the wall so you can mount it to the wall... Like these:

https://www.amazon.com/Drilling-Drywall-Plastic-Anchors-Screws/dp/B0845YKDHV/ref=sr_1_1