I've done researches on the internet but can't distinguish what chip got the role of the H-Bridge.
It's control appears to be very similar to the way latching relays work (impulse driven). What I've read is that they have a permanent magnet like shown here
. Notice the separate SET and RESET impulse.
If that's the case, then if it's single coil driven, a method of reversing the polarity across the coil would be needed (i.e. mini-relay or H-bridge). If it has a dual-coil configuration (or centre-tapped coil) to flip the dots, then no H-bridge is required. It looks to me here that part numbers ULN2804 and UDN2982 are used to drive the coils.
Note that latching relays need an impulse (i.e. 50-100 ms) to operate and would suffer damage if driven continuously at rated coil voltage. I think the idea here is similar (something to investigate).
In any case, once the dots can be controlled, the required code would be very similar to that which drives an led matrix.