They're 32 bit, how do you run this on a 64 bit computer?

If you use Windows just buy the battlenet edition game disc. It worked perfectly for me on Windows 10.

I don't think my version is the battlenet version, what should I do

Then DosBox.
Or you on MAC?

Throw the disk away and spend the $15 for the GoG edition.

I'm on windows 10

The disk is about as useless as just being an old trophy. If you just want to play the campaign, buy it from here or get a free version on the web, won't say where. Plenty of information already about in these forums and I don't like advertising freenium.

If you want to play on battle net, well good news. Disk is just as useless. GoG Warcraft 2 has its own server. Blizzard server does not support anymore.

And, nobody really wants to tech support for a disk in 2019. Sorry to be blunt, but truth is sometimes needed.

What version do you mean to run from disc? Gog war2 have no any discs (I mean CD), is it?
And original war2 disc from Blizzard have no any problems to run from win10 or any other version. (Except palette rainbow or w/e fixed by draw).

There's no problem at all to run x32 application under x64 system, it should be 100% compatible.
The problem can appear when you try to start x64 application on x32 system, not this case...

How do you run those? I get that error a lot with most of my games
Trying to run x32 on x64 I can't afford buying this game again, it's literally 10 times more expensive on gog than what I paid for it

You should just start the exe by double-clicking it's icon or tithing enter to run x32 app under x64 OS, it will do everything itself to run it.
What problem do you have while starting war2 on your win10 x64?
Original war2 bne works with some bugs, but starts fine on win10. You should insert the original CD in your CD-rom.
Can you post a screenshot with error or w/e happening you start war2?

You can also try war2combat - unofficial war2bne build from war2ru team. Should work perfectly on every computer - every OS. Download from en.war2.ru site. Still requires cd-key from gog or original war2 to play on official gog server.

*on Blizzard Battle.Net server (not a GOG server)

Only problem you can have on x64 Win 7\8\10 (only Vista x64 can handle it after some tweaks\updates) is with x16 .exe. Most old Win9x games have x32 exe, but its not a rare when CD use a more old x16 build of installation software. So only thing that not allow you to install Windows version of Warcraft 2 (called Bnet Edition) - is installation process.
If you have origilan MAC+DOS CD version, on Windows you need DosBox or PowerMac MacOS emulator for MacOS X.
Buying GOG version is a way too. Or... well... you know alternate way, if you already have cd with cd-key. If you do not have CD key - i can sell it, i think.

If the installers are 16-bits the problem is with the installers. The game itself is 32-bits, but is using a 16-bit installer. The game itself would run under Win10x64 if the installer program is also 32-bits. But 16-bit installers were often used in Windows 9x (95. 98, Me), as these were hybrid 16/32-bit OSes. Win10x64 is a hybrid 32/64-bit OS, thus 16-bit programs of any description will not run, including 16-bit installers.

I would take the advice offered here and pay the $10-$15 depending on which games you want to buy, as the installer works on a 64-bit OS like Win10x64 just fine. Toss the disks away--you won't need them any longer. GOG specializes in doing the things it needs to do to get older games to run properly in up-to-date OSes. AFAIK, actually, Steam does not do the same, but sells the older original games it still lists in their original state, warts and all. At least, that was the way Steam worked last time I looked at an older game there--hopefully, they've changed that by now, but all I can say for sure is that you are safe with GOG in that regard.