Actually, the destination MAC address in the frame will not be the broadcast MAC address, but it will be the MAC address of the destination host, H2. The frames as they are displayed in both the video and the images are correct.
If the switch does not have the MAC address of H2 in its address table, it will receive the frame and flood it out of all of its ports except the port on which it arrived. All hosts will receive the frame and check the destination address of BBB and compare it to their own. H3 will discard it, however H2 will keep it because its MAC address matches the destination MAC address. This is how devices know that a frame that arrives on their NIC belongs to them (or not).
If the address was the broadcast MAC address of FF:FF:FF:FF:FF:FF, then all devices would accept the frame and begin decapsulating it, because it is a broadcast and broadcasts are intended for everyone.
Now you mentioned that A will NOT know the destination MAC address of computer B. In this example, A does know the destination MAC address. However, if it does not, then another mechanism, independent of that shown in this lesson, would be used to learn this MAC address. This mechanism is known as an ARP request. You can find out more about this at the following lesson:
I hope this has been helpful!