Welcome to freedom from Microsh!t!

WINE—"WINE Is Not (an) Emulator"—is a protocol to run Windows programs on Linux (Bottles is easier to use than WINE, by the way). Flatpaks and AppImages are compatibility-focused variants of Linux programs. None of these boots into Linux itself. Sorry, but there is no way around the flash drive as far as I know, but it's not too hard! I'd question at which step below he messed up. Here is exactly what I did to get it working across a Dell desktop, multiple iMacs of different generations, and Dell and Lenovo laptops, all from different manufacturers and years. You're in good hands here!

1. Buy a USB flash drive; even just 4 GB should work, but if you wanna try bigger/multiple distros than just Linux Mint, go bigger.
2. Get balenaEtcher.*
3. Use balenaEtcher to write the .ISO from LinuxMint.com's downloads section to the flash drive (it can actually retrieve it directly from the URL, or you can download the .ISO live image first onto your PC). Cinnamon is for standard machines whereas the others are better for lower-end, older machines (think ones that seriously struggle to load even basic programs like the browser). Ignore the balenaCloud ad.
4. With the flash drive ready with the Linux distro and plugged in: find the way to access the machine's BIOS and then turn it off; this may be holding F2, F9, F12, or some other key immediately after you boot up the PC. If it doesn't directly tell you briefly upon startup, you may need to search exactly what your make and model needs for BIOS access. Power it up and get into the BIOS.
5. Somewhere in the BIOS (which usually has self-explanatory commands at the bottom), poke around for Secure Boot; many machines already have it disabled, but some may need it to be disabled first.
6. Somewhere in the BIOS, you can set the bootloader order so that the computer boots from the flash drive instead. Or you may be able to just manually pick it to boot into right there on the spot, such as on Asus units. Adjust the boot order, save, and restart.
7. When you can see the very first Linux screen, pick the default/top option. This is a live image to tinker around and check how fast it is, whether it can play sound†, YouTube videos, etc. before you wipe the machine. Nothing you do in this demo mode will be saved anywhere, as far as I know.
8. To install (whether for dual-booting with Windows or deleting Windows), there will be a disc icon in the top-left corner of the desktop. Some people warn that certain Win11 updates in the future may corrupt the Mint side if you try to dual-boot, which I guess is fine if you're just testing; you can always set it to swallow up the rest of the partitions later if you're convinced that you don't ever want to return to Windows. But with that said, remember that you can always find a Windows live image (.ISO) to revert if he just ends up disliking Mint for whatever reason.

Keep us posted on his anti-tyranny journey. Tell us at exactly which step the process goes awry for diagnosis (and make and model), if it does.

Note: On at least some machines, Linux Mint's touchpad may scroll ridiculously fast with 2 fingers; this speed isn't adjustable in its touchpad settings. If this matters to you, you can at least slow it down in Firefox or Waterfox/other Gecko-Mozilla-based browsers through the following workaround:

1. Go to about:config
2. Search mousewheel.default.delta_multiplier_
3. Lower the resulting X and Y from 100 to 70 (or even down to 30, depending on what you prefer); not sure of what the Z axis is for
4. Search mousewheel.min_line_scroll_amount and reduce it from 5 to 2

*If you wanna try many different distros like KDE Plasma, Bazzite, CachyOS, NixOS, etc. without having to keep formatting the flash drive per .ISO, you may consider Ventoy instead of balenaEtcher; it can fit many different .ISOs onto the flash drive all at once (provided there's space for them all; they usually range from 2-5 GB), though it is not compatible with all distros. Presumably all your data is backed up by now, so you can just keep wiping the machine and trying out all sorts of different distros until you like something that you see more than the others. I personally stuck with Linux Mint Cinnamon, though; its automatic Driver Manager makes its comfort level top-tier and just hard to beat, according to many, and it de-bloats its base, Ubuntu (by rapidly evil-ing Canonical), which is based on Debian. So, if you go with Mint, look for .deb files and Debian instructions whenever installing stuff.

†Even if it can't play sound, there's a decent chance that the right drivers and symlink-tinkering‡ can get it working later.

‡In Linux-speak, "symlink" (symbolic link) = shortcut file.