I see that as Canon.
If we think at the Intro of the Show, the Book say the sisters use their Unicorn Powers”.
The word Alicorn was not an official Name, but a more Fan made Name.
Usual Celestia & Co are called “Winged Unicorn”, what are also the Name outside of MLP.
As I know it was not used until the “Magic Duel” (S3E5) Episode where the Amulet, in the Script called “Unicharm” was renamed into “Alicorn Amulet”.
Mean before this Episode, the name Alicorn has not exist for 57 Episodes (good a Quarter of the Show) and after my Knowledge, the first Time an Pony was called Alicorn was “Magical Mystery Cure” (S3E13), where Rarity called Twilight like that, after 64 Episodes.
The Name “Pegacorn” was official used as Description for Chrysalis who was “https://mlp.fandom.com/wiki/Alicorns#Queen_Chrysalis”, what made her in the 5. Alicorn after Dazzleglow (G1), Celestia, Luna and Cadance.
With Twilight, Flurry Heart and Opaline, there are actual 8 canon Alicorns in the Franchise.
I not count Sunny Starscout, because her Alicorn Power is atifical and Horn and Wings are not part of her Body, like a normal Alicorn, but magical Constructs, similar to “Sonic Rainboom” (S1E16), where Rarity had some magical Butterfly Wings, but never was called Alicorn for that.

@BossGriffin
Chapter books and/or comics, and I’m pretty sure the staff re-confirmed it at some point

@NightStalker
Wait, where was this established? First I’ve heard of it.

Everyone forgets Cadance was born a pegasus. Nice pic!