You should be able to make a long-lasting, possibly permanent, repair to this using filled epoxy.
As outlined in previous Answers, you can mix epoxy with nearly any dust to make it a thicker and ultimately stronger material (as well as to modify its working characteristics, e.g. with the addition of talc to improve sandability).
Normally when filling epoxy you just use fine powders. However in this case a mixture of wood dust and coarser stuff, but no large flakes, may give the best results. A mixture of particle sizes results in an 'aggregate' system (similar to concrete) which gives a stronger material than if just dust (or sand alone) would produce.
Because you're using 5-min epoxy as clarified in the Comments, I would suggest doing perhaps two of the divots at a time, so you don't run the risk of trying to work with epoxy that has begun to set up. If you find it necessary do the holes one at a time, there's no downside other than the tedium!
In addition to the epoxy, wood dusts and a mixing tool1 you also want a drill and to have a hair dryer/heat gun on hand if possible.
Here's the entire procedure outlined:
- drill out the ragged holes to make larger, more-easily-filled holes.
- Blow out all loose material with compressed air or through a straw/empty ballpoint tube.
- Pre-mix your wood dust and any coarser stuff into a single pile so you can add it into the already mixed epoxy without wasting time; you will be under the clock every time you mix.
- Heat the hole or holes — not the epoxy — well with the hair dryer or heat gun.
- Mix a small batch of your epoxy, but before you blend with your powders quickly add a small amount to the hole. You'll see that the epoxy will liquefy noticeably when it contacts the heated wood, and more easily soak into the chipboard. Then blend epoxy and wood dusts to a 'stiff batter' consistency approximately — you want something less than a stiff paste; still slightly fluid and able to drip off the end of your application tools.
- When all the holes are filled now you wait much longer than you're expecting for the epoxy to fully cure. I would suggest waiting at least overnight (yes, even with 5-minute epoxy2).
- Mark the positions for the screws and then drill your pilot holes as normal for solid wood, then carefully drive the screws home. I would strongly recommend not power-driving them, unless you have absolute confidence in the clutch on your driver. This is just a few small screws, do them by hand and don't Popeye them3.
You can aim to fill each divot flush by using just the right amount of filler each time but this is a tricky thing to judge. I think it's a better idea to slightly overfill, then flush after setting using a block plane, careful sanding or filing.
1 Note that you'll probably want a stronger mixing paddle than you typically use for straight epoxy (such as the small plastic one included in many epoxy packets). Filled epoxy is much stiffer and harder to manipulate, especially at the consistency you're aiming for here to hold screws.
2 While the packaging of 5-min epoxies may typically state they're cured in an hour the small print may go on to specify that it takes 12 or 16 hours to reach full bond strength at e.g. 24°C (75°F).
3 By this I mean resist the temptation to go "one grunt past tight" :-)