I don't think is Jazz.
So far, I like the music. Despite the fact that you were aiming for the wrong genre and some uneveness in the music, I liked it.
I this is more like a progressive metal. Sounds kinda like it was influenced by dream theater, but in more cheery manner and less metallic.
Also, in the intro, the violin thingy in the background? Might have been a great addition to the music but sounds way too choppy. WAY too much repetition going on and I can litterally immagine you going crazy with the keyboard, cause the violins are too friggin' choppy! smooth it out! (The leading violin was excellent though.)
There are two types of music in my opinion. One is a type with extreme chops, mostly used in metal. And there is another type, which is very smooth. things like classical musics or jazz are usually the ones that belong in the category. In your music, drums with extreme chops and violin with smooth notes, I don't think you've quite achieved the "jazzy" feeling. If this music was aiming for progressive metal feeling, then this is one hell of a music.
I can assure you that you've took a great challenge in mixing both aspects of music because it's not something that can be easily done with ease and create a perfect harmony. I only know few musicians that actually achieved the perfect harmony using both chopiness and smoothness.
I would recommend this music to anybody who plans to make an rpg game like Final Fantasy series, but only if you fix the repetitive violin part. Smooth out the end of each stroke of the violin and this music would be an ace.
This is only my thought, but I would've liked if the piano part was actually piano, not something that is a mixture of electric piano and organ.
Anyway, very nice work! I look forward to your future pieces!