Most people feel that they have certain responsibilities in life. If they achieve those they feel good about themselves, and anything they do beyond that to make the world better is an increasingly imperceptible bonus.
Some people with unusual moral positions or preferences feel responsible for making everything in the world as good as they can make it, and feel bad about the gap between what they achieve and what they could.
In both cases people have a kind of baseline that they care especially about. In the first case they are usually so far above it that nothing they do makes much difference to their feelings. In the second case they are often so far below it that nothing they do makes much difference to their feelings.
Games are engaging when you have a decent chance at both winning and losing. Every move you make matters, so you long to make that one more move.
I expect the same is true of motivating altruistic consequentialists. I’m not sure how to make achievements on the margin more emotionally salient, but perhaps you do?