It's pretty good, but I would suggest putting my character markers. I know it seems repetitive to say:
He said "******************"
She replied "***************"
He exclaimed "**************"
continue ad nauseam.
But it is irritating to a reader. After about 3 lines, I literally made this sound in my mind "WAHWAHWAHHHHHHHHHHHHHHHHH" and skipped all the dialogue, but then went back and read it once I had control again. That is my only advice. I used to write dialogue just like you and it's fine if you want to give the impression that the conversation is happening very fast or is confusing, but the above does not seem to be the case. You can skip a line every now and again, but you really need the majority of lines to have those markers.