I can't send IMs from my computer to NON iPhone recipients.

On your iPhone go to Settings/Messages/Text Message Forwarding and add your Mac Mini to the list. Note that the Mac Mini must be logged in to the same Apple ID as your phone.

iMessages can be sent to Apple devices. Sending SMS/MMS text messages requires a phone. If you have an iPhone you can send messages from your computer through your iPhone as described in Forward SMS/MMS text messages from your iPhone to your Mac or iPad - Apple Support

Also see: What is the difference between iMessage and SMS/MMS? - Apple Support

Happy holidays!