> Is that generally what the rest of you would describe as a Nag screen?
No, not at all. A nag screen is: "You have run this software 3 times, you need to register". Or "Buy this extension to our product" type screens that popup. Install AVG and you will see these popup regularly.
The MAME screen you are talking about provides useful information about the emulation state of a game = very useful. Essential even. Definitely not a nag screen.