Would you get an Internet refrigerator?

Personally, I am not sure how valuable it would be, if you are referring to the concept of it being able to track the contents of what is stored inside using a barcode or RFID. I guess if you get the same stuff, (i.e. milk, cheese, butter, etc.) it could create a shopping list for you and email you. But, not sure I would find that overly useful. I do use a manual app on my phone for my shopping list as I get low on stuff, as I never leave my phone at home, but I'd leave a list at home 90% of the time.

they already make them and they are a complete ripoff. The actual refrigerator part is that of a entry level fridge, and then you get a small LCD touch screen that uses a cheap TN display (common in those $50 Chinese android tablets)

yet when they stick all of that into a fridge (and depending on the fridge, add a cheap $1-2 gpio interface to control things like the ice maker, they then feel a need to tack on an extra $1000 to the price tag for what is at most $40 worth of extra hardware)

also keep in mind that those types of interfaces will mess up eventually, especially the ones that use the resistive touch screen. They offer no way to calibrate the screen and they eventually lose calibration. Furthermore they do not last as long as capacitive touch screens which is especially bas since traditionally, a fridge would last 15-20 years+.

I want a fridge that keeps track of what is in it, internal temps, humidity, water flow and filter status, one that can make, when queried locally or remotely, a shopping list, and either email it or display it, or even send it to the local or network printer. It would take inputs via barcode scanning, RFID scanning, or direct input. and can coordinate inventories with outside databases (what does that barcode mean? Oh, a 1kg tub of X brand 2% cottage cheese...) and shopping apps. I want this device to have a touch screen that can also display information from the network (Local weather, or tap the local thermostat, weatherstation, etc.) I want this device to report error and alerts, including sending emails or SMS or even tweets or chats for critical errors.

I want this integrated with a (several) pantry, wine cellar or beer fridge or root cellar device(s) that would monitor much of the same info. (Contents, temps, humidities, etc.) these devices would also report in the same way. I would also like it to either have the same touch screen display as fridge, or use a local wirelessly connected phone or tablet.

I want this data available to anything that has the API and the right access permissions so that, say a kitchen computer could query the fridge or pantrie(s) to look for ingredients for recipies, or create shopping list(s) based on a recipie(s). I would also like outside devices, (Phones/tablets, even scales, whatever) for inventories, or to correct inventory, monitor environmental conditions, or to remove some items. Say take an apple out, or remove 1.1kg of potato.

NOTE: I am working on this device(s), and have produced one usable prototype.

So, to answer the question? - YES!

I'm confused as to what a "Internet refrigerator" is?

In the future everything will be eventually connected to the Internet, so, for sure! Why not?