If the guy who sold you the controllers only wired the buttons up, then he received the boards with the program on them (and with instructions telling him which buttons have to be connected to which ppins, since it's the program that determines that). Without a program, a microcontroller does nothing. The microcontrollers on arduino boards are programmed with boot loaders, small programs that make USB communication and programming via USB possible. But anything else requires a "main program".
That's the danger when you google for something like "change name HID device leonardo": most results will be pages from people who are programming arduino's. They will assume that people who follow their advice are doing the same thing, that they have written an HID program, and want to change the name. They won't warn readers that clicking "upload" will erase the program present on the board, because that's what an upload is meant to do. They also assume that when they write "upload", their readers know that they mean: "upload the HID program you have written".
The old IDE gave an error when you clicked upload without entering code first, but the new IDE automatically creates an empty setup() and loop() function, which is valid code, so you get no warning.
Your windows device manager still recognizes the controllers as usb devices because the boot loader is still present. But it doesn't recognize them as HIDs because the main program, that defined the HID device, is gone.
The only way I can think of to change the name, vid and pid of an existing device without erasing the program would be to download the contents of the flash memory (not always possible, the programmer may have disabled reading) or the EEPROM (depending on where the chip stores that data), use a hex editor to change the values (keeping the length of the name the same!), and writing that file back. AVR uses little-endian, so a vid= 2341 would be represented as 41 23 in memory.
This topic has information on how to do that: Possible to copy compiled code from one Arduino to another and have it function? - #14 by system
But that means risking another controller, if I were you I would first try to get the "broken" controllers working again. The joystick library (GitHub - MHeironimus/ArduinoJoystickLibrary at version-2.0) seems easy to use, try the gamepad example (I don't have a board with a 32u4 chip so I can't test it).
As for the board file: since they contain arduino micro boards but are recognized as leonardo boards, I would edit the micro and Leonardo sections in the boards.txt file, and select one of the two as board in the IDE, see what works; You don't have to select a programmer for a normal upload, that setting is only relevant when you choose "Upload using programmer" in the sketch menu.