The Hindu gods, in a Buddhist procession

The organising committee invites volunteers to dress as the gods — Brahma, Vishnu, Maheshvara, Indra, Varuna, Yama, Nagaraja and others — and walk in the line. What they are enacting is the Buddha's arrival, after his enlightenment, at the grove of Lumbini, and the gods' reception of him there. A Newar processional song describes the scene: Brahma sweeps the ground before him, Saraswati spreads a carpet, Kubera scatters wealth, Vayu fans him, Agni burns incense, Varuna makes water flow, Mahadeva beats a drum, Narayana blows a conch, Yama clears the way with his staff and Indra holds an umbrella over him.

The offerings are the gods in shorthand

The correspondence is carried literally in what the walkers hold. Each object in the line is one of the deities, compressed into a thing you can hold in your hand:

a broom — Brahma, sweeping the ground
a conch — Narayana / Vishnu
a drum — Mahadeva
a parasol — Indra, king of the gods
a staff with a snake — Yama, king of the hells
flowing water — Varuna, the naga king
incense in a pot — Agni, god of fire
a flag or banner — Vayu, god of wind
coins or five jewels — Kubera, god of wealth
a carpet — Saraswati, goddess of wisdom
a yak-tail whisk — the Buddhist monks fanning the Buddha
milk-rice — Sujata, who fed Siddhartha before his enlightenment
an alms bowl — Anathapindaka, the merchant who built the Jetavana monastery
fruit — the monkey of the Kimsuka forest
a five-coloured thread lamp — the five delusions burning away
sugarcane juice — the nectar of the gods
printed dharanis and mantras — praise of the teaching itself

Why it is not a contradiction

A Buddhist festival led by the Hindu pantheon reads as a muddle only from outside. Newar Buddhism did not survive the last thousand years by drawing a hard boundary; it survived by absorbing. Scholars argue about whether that was theological confidence or a defensive strategy — a text with Mahadeva's name in it was a text less likely to be destroyed — but the effect is the same, and Matya is where you can watch it happen in the street. The gods are not competing with the Buddha here. They are in the audience.