Looking at the Aliexpress pictures, you can see it’s a modified version of a standard 7/8-lug switch. It’s still split into two ‘sides’ to mimic a wafer switch, each with its own ‘common’ connection to three sets of contacts for ‘neck’, ‘both’ and ‘bridge’ positions, but as on a 7-lug switch, the two commons are internally connected to a single common ‘common’, rather than the two commons having to be externally connected together.
In the picture/diagram you deleted, the links for connecting the ‘neck’ to ‘both’ contacts on one side of the PCB were done externally when wiring the switch. The same for the other half of the switch PCB, where the ‘bridge’ and ‘both’ contacts were joined externally.
On the 3-lug switch, the connection between the ‘neck’ and ‘both’ contacts on one side, and ‘both’ and ‘bridge’ contacts on the other side of the switch are done on the PCB, so you only need to make one solder connection per pickup and don’t have to worry about making the link.
There are two ways to wire a standard 7 lug (or 8-lug) switch. If we number the terminals on a 7-lug as
1 2 3 4(C) 5 6 7
where 4 is the common (C) output connection, then you can wire it:
a} 1-2 3 4(C) 5 6-7
or
b) 1 2-3 4(C) 5-6 7
where the ‘-‘ is the link. For a) you’d wire the neck pickup to the side of the switch nearest the bridge, and the bridge pickup to the side of the switch nearest the neck. For b) you’d wire the neck pickup to the side nearest the neck and the bridge pickup to the side nearest the bridge.
The 3-lug switch is wired as type a) with the linking all internal, making it much simpler to wire up. It makes it a less flexible switch, but for a straightforward 3-way switch, it’s fine and no different to a 3-way box toggle switch in concept.
Your deleted pic showed a type b) wiring arrangement.
For completeness, on an 8-lug switch
1 2 3 4(C1) 5(C2) 6 7 8
Where the common connection for each side of the switch, C1 and C2, is separate, you’d wire and link it as either
a) 1-2 3 4(C1)-5(C2) 6 7-8
or
b) 1 2-3 4(C1)-5(C2) 6-7 8
So the 3-lug switch is both similar, and at the same time quite different, to a 7-lug or 8-lug switch.
A logical variation on a theme and for a 3-way Tele switch, a 3-lug makes perfect sense. They’ve simply modified a 7-lug PCB by drawing the links on the board, though it would have been less confusing to have simply laid out the PCB so there were only 3 holes and three lugs. But I suppose it allows a common pre-etching board shape to be used for 3-and 7- lug switches and so saves money and supply complexity.