Electrical – How to ground a kitchen exhaust blower fan

Recently our kitchen exhaust fan stopped working, only humming and not moving. In the kitchen there's a butterfly damper, the exhaust switch is on the vent hood, and the motor and exhaust fan are on the outside of the house.

Did some troubleshooting with the motor, tried cleaning it up but it's DOA. In doing some research it appears this fasco motor is from the 60s(give or take). I called some manufacturers and found a supposed replacement since that model isn't produced anymore. Unfortunately I didn't look over the diagrams and the replacement didn't have the same mounting bolt holes.

I did some digging and found a replacement motor, ordered it and it fits (it's a fasco d367). But I noticed the new motor has a big warning to ground it, but it doesn't have a ground wire. I don't see the two squares on the label saying it's double insulated.

The original motor didn't have a ground wire either, but the dome and components had a ground wire and so were grounded(partially disconnected in this pic when removing the motor).

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So is the ground wire on the metal dome enough to ground the motor through the case? Or is there something else I need to be doing to properly ground the motor?

Thanks!

Here are some pictures of the new motor for reference.