Mains electricity is not a toy!! Low voltage DC is a toy, which is how you got misled.
Mains will steal your girlfriend, wreck your car, cancel your fire insurance, burn down your house and kill you. It is a completely different beast. (It's a very slightly less psychotic version of mid-voltage DC, which made a serious college try to kill 3 astronauts the last time it was trifled with. AC, at least, has a zero crossing that will often snuff arcs).
Anytime you get an urge to do something with mains electrical, put down the soldering iron (you'll never use it), come here and talk about what you want to do. We'll run you through it the right way, that meets Code, will save your fire insurance, and will be safe. Humanity's best-practices at handling mains power safety (Code) are so refined that it looks easy, and that makes mains AC seem harmless. As such, Code can seem stupid. It's not.
I'm sorry to give you the finger-wag, but you specifically asked how to connect AC live, AC neutral and ground.
But you're in luck
That's a Barrel connector. Mains power would never be on that because it wouldn't have the dielectric strength. The weird lump in the power cord is not merely to annoy you, it's to knock AC mains power down to low voltage DC.
By the way, the reason so many manufacturers do that, the thing with the wall-wart, is it allows them to sidestep the bulk of the UL listing process. They only need to clear the low hurdle for low-voltage DC machines, then they toss in a commodity off-the-shelf wall-wart that somebody else already got UL listed. That's why wall-warts almost never have any labeling to say which equipment they go with.
The Electrical Code has sweeping exemptions for low voltage devices under 30V (talking to you, NASA) that are also under 55 watts. Your device probably falls under that exemption.
You only need to figure out how to convert mains to the correct low voltage safely (e.g. By simply using the power block that came with the machine), how to site the power supply (plugged into a nearby receptacle is pretty safe), and how to connect the wires.