It'd make sense for them to offer some way to do this online and pick up in-store (or, hey, ship directly). But, it might bring people into the stores or you may have people that want to "feel" examples of the material they're printing the item in (assuming it's offered with different options, which would be a good idea).
[0] I'm thinking FDM here, mostly, but you're basically taking a material, heating it to the "right" melting point, applying it to a surface where gravity and controlled cooling cause the layer to adhere securely to the previous layer. The printer can only print as fast as it can reliably melt/adhere the material, any faster and you either under-extrude or fail to adhere and end up with spaghetti.
NOTE: I tried to pitch this to a former employer of mine and they didn't really see the market.
If it took 15 seconds, or even five minutes, to 3d-print a model like that on a desktop machine, then sure, there might be something here. But the Stratasys J750 production printer that Shapeways uses for multicolor prints [0] requires, per its user manual [1], "between several hours to several days" to complete a print, depending on size. It also weighs half a ton, needs a room and about 3 kilowatts to itself, and those are where its environment requirements start [2] - not to mention that the uncured printing materials appear to be quite toxic, judging by the bulk of safety, first aid, and hazardous materials handling discussion in the user manual. And that manual is what you're meant to use as an aide-memoire after being trained by a Stratasys field engineer in how to operate the machine at all.
The machine is apparently designed mainly to print anatomical models accurate enough for surgeons to practice on them, and in that context its engineering requirements are reasonable. They're also reasonable for a company like Shapeways, which entirely revolves around 3D printing and can arrange its physical plant to suit. I won't even say it's impossible to cram something like this into a strip mall, but it'd probably need to be next door to an outpatient MRI clinic or something like that, to get the services it needs without the cost and permitting of having the runs put in - you'd have to pick the site to suit the process, and GameStop locations aren't picked that way. And even after all that, the print time is still a killer.
In theory, sure, it would make sense. But in practice the tech just isn't there yet. About all that leaves, I think, would be "BOPIS for Shapeways", and I doubt that'd be a big enough draw to be worth the trouble - at that point, it probably makes more sense for the studios to do something like Hero Forge, and cut GameStop out entirely.
[0] https://www.shapeways.com/materials/multi-color-polyjet
[1] https://www.stratasys.com/-/media/files/documentation/polyje...
[2] https://www.stratasys.com/-/media/files/printer-spec-sheets/...
You can only slightly "buy your way out of the speed problem", which is as much dependent on the material as it is the capabilities of the machine. An 18 hour print for a small item is not unusual at all, for me, but I'm on a pretty simple printer.
A stratasys-style machine wouldn't make sense for this application. I think "high-end desktop quality" FDM would suffice for accessories/GameStop (with, perhaps, an option to get items printed in aluminum/other exotic materials shipped -- partner with someone), so the aim would be to find a reliable, enclosed (with appropriate filtration[0]), FDM (or similar price/quality), pick up 3-5 of them per store -- different sizes -- and spend a mint building software for your customers to use to interface with the printers[1] and automate the hell out of the ugly parts of the printing process (print-bed surface prep/part removal, maintenance and cleaning). And make absolutely sure the model has every convenience feature (like bed leveling, temperature controlled build chamber)
I'd probably limit material types to one (production) and one (support, when necessary). Optimize all of the hardware for the printers to the specific characteristics of that material and choose a material that prints easily/quickly -- PLA is a reasonable choice, prints pretty quickly but is brittle/fails over time and has a low melting point, ABS has several toxicity concerns and is finicky as hell to print with, but it's cheap and when it prints "right", it's durable.
It sounds crazy to do something like this with desktop 3D printers, but it makes the most sense. $1000 will get you one hell of a box with the ability to print in multiple colors and with more than one hot-end. It's probably, as you mention, not quite there yet -- I know from personal experience, messing around with the slicer software can take some time. There'd be a lot of software to be written and probably some additional hardware to design to fit the purposes of the stores printing needs. But, I guess you'd give the staff something to do while waiting for customers to not come in and buy games. /s :)
While they're at it, throw in a large CNC/laser cutter, re-tool to sell dev boards/robotics equipment, replace "Game" with "Hacker" and open up several hundred hacker-spaces around the country. Perhaps that would have worked better for Radio Shack. But I'm only half-joking -- every time I walk into small-time game/hobby/computer shops I find that the (often young) staff there are makers and would fit right in with a little training.
[0] This, too, depends on the material. And you might need to call in the lawyers/etc to figure out how things are going to have to be designed to avoid a future class-action from your employees/customers due to exposure to fumes. ABS is known to be problematic; it's also cheap and has many other desirable properties.
[1] The good news is that there is a ton of open-source pieces to start with.