Burst Mages are mages with insane Burst,
Neeko Burst is actually in par with most burst mages.
The weakest one being Lissandra because of her low base damage and Ratio.
Heck I won't even consider Lissandra a burst mage with how she stands right now.
Neeko is pretty much between Annie-Lux with a Veigar Level of burst.
480 (+ 90% AP)+220 (+ 40% AP)+650 (+ 130% AP)+170 (+ 60% AP)= **1520(+ 320%)**
And to be able to dish out all of these damage you have to take into account she has to hit the full duration of her Q + being in melee range for her R.
She is relatively squishy if she goes for the full damage build.
But I think she is pretty balanced for a burst mage, since of the damage can be dodged.
I personally think most burst mage needs their damage buffed, alot of them are relatively risky especially into an assassins mid.