I got it working. Here's what I did:
Working as administrator account, go to Plugins
Find "Delivery Limitations Plugin" - Click on details
Find "Client Delivery Limitation Plugin" - click on settings
Check the box beside "Extract the viewer's operating system and web browser information using phpSniff" to select it and save changes.
Now, go back to the banner you don't want to show to mobile devices.
Go to "delivery options"
Find "delivery limitation" - choose "client - useragent" and "add"
For "Client - Useragent" choose "regex does not match"
In the field below it, add the devices/browsers etc. that you want to exclude.
Click "Save Changes" and it should show the banner to desktops only.
There could be a better way, but this is working for me.
Hope this is correct and it helps someone.