It implies that the device is not a "new console" rather some device that runs packaged software.
I think the days of consoles as we had known them are basically over. Everything is just a computer now.
Only real difference between some newer consoles and computers is a lot of the time Computers are cheaper
how is a computer cheaper than a 300 - 500 $ console
Computers are usually around 1K $ park withouth a screen
You don't buy a console without a screen, why is a computer any different? If you want to use display comparisons, then you could say that on average, a console setup is more expensive than a computer setup, as many people spend more for their television than the console.
Cost equivalents for consoles to computers are very close, on a price of manufacturing basis. Modern console price per unit is determined by the cost of the run and the projected royalty incentive from sales on their respective digital marketplace. This means that a console can be priced with a 10-20% markdown below cost if the royalty payments per unit are expected to say... add 30-40% per unit over the life of the unit. You do not see this type of pricing in computers with exception to the low end retail market, where computers by large manufacturers like Dell or HP are selling computers loaded with trial software and have their own storefront on the Windows Store. They can sell those computers at a very low cost because of the expected royalty return of bundled software and promoted apps in the online store.
This idea that you would need a high end computer to run current console games is simply not true. You can use a 5 year old mid-range computer or a current below mid-range computer to run any console game. This matches perfectly as console technology to software capabilities is slow, and consoles have historically matched to just below mid-range computers of their era. However, what you are saying had been true in the past, but is not true right now. There are three main factors in play here, but the end result is a shrinking in advancement of technology when it comes to computer games. The first is the shift away from desktop computing to the mobile market, the second is shifting gaming market from desktop computers to consoles (developing on lower-end systems) and then the fact that technology has not really progressed that much (in comparison to the past) for about 12 years now, which was when the Quad-Core CPUs hit the retail market.
The emulator comparison for old systems is not comparible in the way you put it either. The requirements are due to the emulator itself, rather than the software. It should be obvious that devkits for those systems were computers of that era and they had no problem running those games. They did not have devkits that were using technology 20 years into the future.