What determines whether Chess.com will compensate points for games against engine cheaters?

FWIW, it makes sense to do it like GYG said, and not refund everyone. When a cheater is banned, rating points are removed... over time this can cause rating deflation. An important element of giving points back (the most important IMO) is countering that deflation... sure being given points is nice psychologically, but your rating will recover on its own even if they didn't refund anything.

If a cheater is rated 3000 when banned, for example, then you may be "deleting" around 1000 points from your pool, in which case giving back no more than 10 points to 100 people would make sense... just an example.

...

just report them normally

why does anyone need a forum for that

giving priority IN the reporting might make sense though

There are few thousand reporting every day, how can chess.com can cope with that? 

To discuss the topic of cheating and related topics any further, please join the Cheating Forum: https://www.chess.com/club/cheating-forum

To answer the question, however, refunds go back up to 3 months or 100 games in the cheater's archive, whichever happens first. Anything older than that is considered to be old history.

This isn't perfect, but due to the way the rating system works, it doesn't need to be.

In Elo-type rating systems (and the Glicko rating system that chess.com uses is an improved variant of Elo), your rating will narrow in on an accurate rating level that matches your ability as you continue to play games. A temporary shock to your rating (such as losing unfairly to a cheater, or playing while tired or otherwise impaired) will quickly disappear.

The lower your rating is, the more points you gain from winning and the fewer points you lose when you lose a game. As your rating climbs, you gain fewer points when you win and lose more points when you lose a game. This will balance out when you reach a rating level where you obtain results comparable to others of the same rating.

In other words, the rating system keeps adjusting your rating towards the point where you can expect to score 50% (counting a draw as half a win) against similarly-rated opposition. A temporary shock to your rating (such as losing to a cheater) will move you away from this point, but it won't take very many games before you get back to this point.

This means that rating refunds aren't really necessary. They help you feel better about the loss, but they have no lasting impact on your rating, other than an overall minor inflationary effect on the broad rating pool as a whole (note that there are many other inflationary and deflationary effects on the rating pool, and they seem to be roughly balanced).

This is also why good runs that increase your rating and bad runs that hurt your rating never last unless there is actually a lasting change in your overall strength of play. A good run will result in you being overrated, and the rating system will drag you back down to reality. A bad run will result in you being underrated, and the rating system will drag you back up.

The only way to make a lasting change to your rating is to make a lasting change to your overall strength of play - to get better, or worse. Either that or to simply stop playing to preserve your rating as-is.

Note that rating systems are not an absolute metric; rather, they are useful only for comparison within a rating pool. This is a major part of why people have different ratings on different sites, in different time controls, or even different OTB ratings with different federations (USCF vs FIDE, for example).

For more information on the Glicko rating system, see https://en.wikipedia.org/wiki/Glicko_rating_system or https://www.glicko.net/glicko.html.

To discuss the matter of cheating, cheat detection, and any related topics, join the Cheating Forum: https://www.chess.com/club/cheating-forum 

Moderators are just other users like all of you with very limited extra insight into what goes on. We can't give official answers.