I went and looked at nitsuja's runs in comparison to this run, and the others exhibit a much higher degree of precision and entertainment. In particular, item collection is manipulated to a much greater degree there (in the SB2 run several bomb and flame powerups are collected before the end of the first level to your one and one, a feat it takes several levels to do here). I spotted at least one bomb which didn't seem to do anything of substance and one instance where you go to collect an item at the end of a level instead of going to the exit which is just appearing (this is 1-5, I think).
Without trying very hard, I was able to achieve
2:28 unassisted on the first level (without the use of the clock stop item, as seen in the run; without seeing it in the run I'd estimate a time of about 2:26). (By the way, use the same version of the emulator as for the run to see that).
Basically, it's clear to me that this run doesn't exhibit the level of technical polish needed to be publishable.
I must vote no on this, but I would encourage you to continue to experiment with the game and see if you can achieve a higher level of precision than seen here.
By the way, the movie file claims it's for Super Bomberman 3, but it plays back normally on 4.
EDIT: Apparently, that unassisted run of 1-1 is 419 frames faster than axelito's attempt. Draw your own conclusions.
