It's impossible for your Alolan Raichu to be shiny because the Alolan Raichu from this side mission is programmed to never be shiny. The fact that it has no shiny icon or sparkles are proof that it isn't.
I think I know why you're confused, though. The top Alolan Raichu sprites on PokémonDB look like this:
Those are images of how it appears on the 3DS, likely in bright sunny lighting.
Meanwhile, in Legends: Z-A, Alolan Raichu looks like this at night:
So since the 3DS images of Alolan Raichu are unusually bright and your Alolan Raichu is possibly in a dark environment, your Alolan Raichu looks more like the shiny sprite, but it isn't actually shiny. It's just the result of differences in color display. If you're ever confused by the color of a Pokémon, you can confirm whether or not it's a shiny by checking for the shiny icon or for sparkles.
