Not sure what it's supposed to parody, but I'm getting some serious Zone of the Enders vibes.

Fairly certain it's Gundam Vs Gundam.

Kanako's Onibashira Formation looks like those of Zabanya Gundam's Rifles and Shields Bits formation in before releasing a huge charge shot to the ELS during the decisive battle on the movie. While hijiri is using Burning Finger of G Gundam

Looked like Yuugenmagan to me for a while.

00 Quanta [Quantum Burst mode] parody from the game Gundam Extreme VS. with Sanae being 00 Quanta.

I definitely want to see a Touhou game in this style some day... Sky Arena is the closest thing so far to the Gundam VS style of playing but Sky Arena is lacking in combos and melee movesets. Also Sky Arena is purely just flying, the boost factor is good but useless for anything else but just flying closer or away from the enemy.