In the Iliad and the Aeneid, they're funeral games, which were an important way of honoring the dead; this was a Mycenaean custom in the era when the Iliad was set, and Virgil was deliberately echoing Homer, so the funeral games for Anchises are intended to remind you of the funeral games for Patroclus. The emphasis on these games--as well as the detailed descriptions of the prizes given--illustrates the characters' reverence for the deceased, especially the grief felt by Achilles and Aeneas. They're *not* orgies.
Don’t know on the games but I do think it’s helpful to understand most of these stories weren’t “written” in Ancient Greece. They were part of an oral tradition I.e. stories recited by bards.
So some of the language and structure is built almost as a mnemonic device to help someone recite it consistently from memory and can therefore be quite repetitive. The one that sticks in my mind is Athena in the odyssey. She’s never introduced as “Athena” it’s always “Athena-the-grey-eyed-goddess”.
Wrt the language, what we read now is just translations of transcriptions and the translators put in “archaic” words just to set the mood. To my mind there’s no reason a modern translation wouldn’t be equally valid: the 21st century English term for something is not really any further removed than the 19th from a story told 3000 years ago in a dead language.
> The games themselves seem at times unimportant to the overall story. [...] Am I missing something within these games that is imperative to understand the greater narrative...?
Like the Shield of Achilles sequence, the purpose of the games is not to 'advance the plot' but to reflect on what has already happened in the poem, and what has happened in will happen in the historical narrative from which the plot of the epic is drawn.
Epic poems are narrative poems, but they are not simple narratives; their primary aim is not to present plots. The mythology around the Trojan War and the founding of Rome was already widely known, just as Christian mythology wasn't anything new in Dante's time or in Milton's. The purpose of epic is to give fresh, coherent poetic expression to those myths in ways that go way, way, beyond mere storytelling.
Do those 'temporary' players get clearly described physically?
Because when I remember that a) Greeks played most games naked and b) homosexuality wasn't feared at the time, it almost could be a euphimistic description of gay orgies.