Here's another save state, I have the power bracelet now and I'm on the same screen as the guy who made the vid started from.
http://rapidshare.de/files/5496161/Zelda_no_Densetsu_1_-_The_Hyrule_Fantasy__J_.fr1.html
Edit: I haven't really done much testing to prove this, but after studying the vid a bit more, I'll make an educated guess about how it works. You can't abuse this glitch to just get taken wherever you want. When you use the whistle, you get taken to the right from the screen you're on to the screen with the labyrinth. With this glitch, you get taken to the same part of the map as you would have been taken, except that the whirlwind didn't get a chance to take you right a screen, so instead you'll be one screen to the left of wherever you would have been taken, except that it'll look and feel like the screen you were on when you blew the whistle. If you enter a cave or stairway after doing the glitch on the screen that it looks like you're on, you'll enter whatever cave or stairway is on the screen that you're really on. If there is no cave or stairway on that screen, it'll just take you to that screen and create a cave or stairway on the screen that leads nowhere. The only thing in the vid that doesn't support this theory is how he entered level 8, it just doesn't make sense why that happened. The only explanation I can think of is that for no reason at all, the programmers decided to put a second entrance to level 8 on the screen to the left of the normal entrance, but you can't normally access it because there's nothing bombable or burnable on that screen.
Edit: Oh yeah, and if you're wondering how he got taken back to the start, that was when he warped to the screen left of level 3. Then he walked down from there, so it took him off the map, which apparently causes you to reappear at the starting screen.