As a lifelong Tolkian stan, I very much believe the Charge of the Rohirrim at the Battle of the Pelennor Fields is the greatest passage ever written. 25 years after first reading the LOTR this passage can both make my eyes misty and get my blood pumping at the same time. The preceding chapter concluding with Gandalf and Witchking confrontation interrupted by the echoing horns is masterful as well leading into the greatest hype moment of literature.

I was randomly thinking, are there any moments in videogames that bring this same sense of profound triumph?

The closest thing I can think of off the cuff is a small transition in Halo 4. For the longest time I remembered it as a cinematic cutscene, but after looking it up it's an in game engine sequence after Chief sneaks into the slip space bubble of the Didacts ship and follows him to earth.

You basically come out of slip space and hear over the comms that the Infinity is battered and earth is looking fucked. Chief comes on the comms and announces himself and Lasky is like WTF, how are you here??? Previously the dickhead commander of Infinity had abandoned Chief on the planet Requiem for insubordination, so the fact that he's somehow here to save the day with a badass nuclear bomb is shocking, but only briefly. The mood quickly changes from desperation to hope as everyone rallies around Chief to go on the attack.

Not quite the same but the closest I could think of.

Halo 4 sequence:

There is a loud crackle and the streaked sky above returns to normal. Earth can be seen overhead.

Cortana: "Cherenkov radiation fluctuating! We're coming out of slipspace!"

Fleetcom Watch (COM): "At current velocity, hostile will achieve Earth orbit in approximately 4 minutes."

Infinity Comm (COM): "Roger. Battle Group Dakota, close on the Forerunner vessel."

Cortana: "Infinity must have warned them!"

John-117: "Sierra 117 to UNSC Infinity. Captain Del Rio, do you read?"

Thomas Lasky (COM): "Chief, it-it's Lasky. Is that you?"

John-117: "Affirmative, Sir. Where's the Captain?"

Lasky (COM): "FleetCom didn't take too kindly to his abandoning you on Requiem. I'm afraid I'll have to do."

John-117: "The Didact's got the Composer. We're in a Broadsword carrying a HAVOK-grade payload, on approach to deliver it."

Lasky (COM): "Let's see if we can grease the wheels for you. All ships! Prepare to engage!"

Midnight – Campaign level – Halo 4 – Halopedia, the Halo wiki https://share.google/BKV9fTQlzdRy7bKME