Extrapolating from the real world... playing games.

The possible challenge level of games scales with the ability of designers and opponents, and the time designers and opponents have had to develop their skills.

The challenge level needed to keep players engaged scales with ability level of players, and the time they have had to develop their skills.

If all the players and designers belong to the same "Elder race" and are equally immortal, experienced, and intelligent their is a natural match between challenge levels and the players will never get bored.

As for the actual games, they are actually probably beyond our ability to even understand, but generally in fiction playing god, meddling with primitives, power games with your peers, and various scholarly and artistic pursuits have been used. But that is probably because they are easy to use in stories and remind people of the old gods. I'd recommend leaving the details of actual games vague and focusing in the consequences such as elation, disappoinment, rivalries, alliances, and so on.

Extrapolating from the real world... playing games.

The possible challenge level of games scales with the ability of designers and opponents, and the time designers and opponents have had to develop their skills.

The challenge level needed to keep players engaged scales with ability level of players, and the time they have had to develop their skills.

If all the players and designers belong to the same "Elder race" and are equally immortal, experienced, and intelligent their is a natural match between challenge levels and the players will never get bored.

As for the actual games, they are actually probably beyond our ability to even understand, but generally in fiction playing god, meddling with primitives, power games with your peers, and various scholarly and artistic pursuits have been used. But that is probably because they are easy to use in stories and remind people of the old gods. I'd recommend leaving the details of actual games vague and focusing in the consequences such as elation, disappointment, rivalries, alliances, and so on.

DoubleDoubles answer mentions gambling. Gambling is addictive, which raises the point that while the Elder Race could no doubt resist and cure addictions, they would have no real reason to do so, if the alternative was boredom. As such they could have severe gambling or gaming addiction that would help them resist boredom. But from which they could recover almost instantly if required by circumstance.

If they have no real reason to resist addiction the same goes for compulsive behaviour. H.P.Lovecraft had a Great Race that was rather compulsive about the study of history and the events and people of different time periods. Similar obsessions could keep an individual or even entire race busy for a long time.

There is a simple cure to "having seen it all." You can simply forget some of what you have experienced. An Elder Race would have techniques that could put some parts of their memories in cold storage. They'd still have access to the memories, if they needed them, but in the mean time they could re-experience things for the first time as many times they wish. An ability to edit their own memories would also make them pretty good at infiltration. Infiltrating primitive societies could well be a favoured pursuit.