Is it possible to run old adventure games like Simon the Sorcerer bought on GOG on a real old PC? I don't see any original .EXE files in any of games running through SCUMMVM so I'm assuming I'll have to use one of these sketchy "abandonware" sites instead?

Unfortunately, you're right.
While most DOSBox games come with all the original files, SCUMMVM may or may not come with the original executables. If you don't want to hunt for the original discs on ebay (which may cost a fortune), you can buy the game on GOG and look for exes somewhere else.

I have checked and both Simon 1 & 2 are available from a non-sketchy site, so at least there's that. ;)

If you already own a game (here or elsewhere) you should legally be fine if you use an archived version. (I'm not a lawyer for international copyright law but from what I've heard, companies strike distributors rather than users anyway.)

Unfortunately GOG is doing their own customers a great disservice by randomly removing files from old games releases. Those files doesn't take much from the size of the installer, nor hinder scummvm from running the game. They could just simple left them there to allow people to use those games on old machine. They are informed of the issue and how much users want all the files in the release, still they keep doing that on occasion (it seems they don't have a clear policy on that, some games have the files, other dont's). I guess if we want things done right we should ask professional to do the job.

I'm not sure GOG are the ones who made that descision. If I had to aim a catapult loaded with fecal matter at either GOG or MojoTouch, MojoTouch would seem like the more deserving target...

You are right in saying that Mojo Touch doesn't care, I wouldn't doubt that and this anniversary edition is a proof of that. But GOG has an history of neglecting customers of proper and complete release for old games, expecially when we are talking about scummvm, so I stand my case. In particular, the original version of simon the sorcerer is provided by GOG and it was already there before the mojo touch version came along.

Well unless a staff member that was preparing Simon the Sorcerer drops here we can keep guessing why they removed .EXEs. On the other hand I'm a bit surprised that there are SCUMM games that still have them, never seen one but I don't have that many adventure games anyway. Aside from Simon 1 have only free ones if I think about it.
Well I'll check some websites for Simon executables and test them with GOG files this weekend and I'll let you know if they work. Kinda afraid there will be some protection mechanism (not likely) or the CD version will look for files on CD drive (and it's going to be a pain), but I'll have to find the right .EXE first (so far mostly FDD).

And by sketchy abandonware sites I meant that Simon series are not an abandonware since you can buy them so it's just normal warez.

If you absolutely, positively have to have the .exes you could buy the original games from Adventure Soft's online store and have them shipped to you. (The Simon The Sorcerer Double Pack with Simon 1 & 2 is £18.09 [including postage].)

I'm not saying that this would be the best course of action or that you should have to, but at this point I feel like I should at least point out the option.
(It would be entirely possible that you make like 40.k zloty a month and want to play the game on an old machine for the retro feeling. ;) I don't know...)

I've seen that package when I was looking for a way to launch it, it is way cheaper on my local ebayesque website. I was actually thinking about buying it for a minute or two, but I really don't like buying stuff twice. Plus I'm pretty far from being rich so I try to keep my urges reasonable.
Anyway back on topic.
I found diskette .BAT files without a problem but had some trouble with CD version, finally found some pirated version of Simon Double Pack that HeartsAndRainbows mentioned and tested it all. Good news is it all works without a problem with the rest of GOG files. Not so good news is diskette version have manual based DRM with some graphics that are poorly visible on scans I found. Just the way they intended it.
I don't think I can post links to manual or .exe files (intellectual property), but I think that if someone needs them with that much information he/she can find them.