I have tried reproducing this in other emulators and I always lose. I'm pretty sure I'm getting the correct input, you can tell when the paddles both fall at the same time, but the game plays differently.
In particular, pterry starts in a different position on screen. You can see this quite clearly here:
The bird starts 1 pixel to the left in Bizhawk. I captured this using the Stella emulator, which has a frame advance feature in it's debug mode. The birds X position is at $61. In BizHawk on the frame the bird appears, the value is 0x4D, in Stella it is 0x4C. Other emulators agree with this position.
But you don't need frame advance to see the differences, here is a another screen shot of the countdown, the number '1' is pretty clearly one pixel to the left in Bizhawk:
It's not the ball that is positioned wrong either, it is at 0x55 at $5B in both.
I suspect there is an emulation issue in Bizhawk.