Making GIL via questing instead of selling

[Squintina]

Sort of...
While there really isn't a good way of making gil directly via quests (as most quests are limited anyway and the few repeatable quests that do exist aren't really good for making gil), if I rephrase your question to "is there a way of making gil without being a crafter or gatherer?" then your options are greatly enhanced.

Here are the options I see:

1. Challenge log
Not a huge amount, but it's ok

2. Selling quest REWARDS
By the time I got to 70, I already had about 3 mil. This was mostly from selling quest rewards from MSQ instead of using them to gear myself up. Instead I joined a hunt linkshell to use poetics to gear myself in augmented ironworks gear (which I used for 50-59), and augmented shire gear (which I used from 60-70, replacing only with dungeon drops and then eventually the job quest rewards).
I got a few more later on by going back and doing side quests on a second job with the same principle - if a quest offers up rewards, choose gear, sell it on MB.

3. Making use of currencies
Whether it's by dungeons, potd, roulettes, hunts, you can get a variety of currencies.
There are so many ways to get currencies that I couldn't possibly list them all...but I would HIGHLY recommend joining a hunt linkshell - or at the very least doing the weekly hunting bills from the hunt board.

You can then use that to buy materials to sell on the Marketboard.
Or to buy unidentified soil/ore to exchange for gardening soil, to then sell that on the marketboard.
Or to buy gear, to turn that into GC, to then buy materials from the GC, to then sell that on the marketboard.

So don't let your currencies stay capped. All currencies can be turned into a marketboard-able item somehow. (except maybe beast tribe and wolf marks, but I'll be honest I just haven't bothered to figure out how to make money from them yet. It's probably still possible)
Allied seals? gear -> GC -> mat.
Centurio seals? Materia, or gear -> GC -> mat.
Poetics? gear -> GC -> mat or unidentified -> gardening.
Creation? gear -> GC -> mat or selling direct creation mats.
Mendacity? selling direct mats or buying gear to turn into GC when they enable it later.


4. POTD
While I personally dislike potd, my husband didn't and a large portion of his gil came from being lucky to get rare items from the hoard sacs, which he then sold on the marketboard.

5. Retainers
You retainers can get you items. If you like constant gil, figure out which mats they can directly gather for you to sell. If you want a gamble for better chances, the quick and long exploration ventures (the ones where you're not asking for a specific item) have chances to get rare minions and dyes.

6. Eureka
Eureka = grade 5 combat materia.
Go to mutamix to try to turn it into grade 5/6 crafting/gathering materia (you will need a crafter high enough to unlock transmutation, but it's pretty low - like 19 or something).
Or just selling rewards from lockboxes. It's not a huge amount, but it does add up over time I suppose *shrug*.

7. Maps
Treasure maps to try to get into the 2 special dungeons which can have some great rewards.

Conclusion:
I think you're noticing the pattern. While it still relies on selling, there are a variety of ways to get things to sell without doing crafting or gathering. It won't be the hundreds of mils that those people have, but it can easily get you to 10+ mil and sustain you for food & pots once you get to endgame raiding.

And you can take this from someone who hasn't really done much crafting/gathering. A little here and there,but mostly for the purpose of leveling. And I pretty much stopped around level 15 and then moved on almost entirely to leveling via supply & provisioning (which I buy off the MB, I don't make/gather the items needed)and beast tribe quests, so I actually lose money from leveling them lol.
But doing the above sustains me being able to buy my way through S&P, buy all the things I need to do endgame raiding, and any other things I ever felt I needed.