In standard STP, the TCN originator sends a TCN upstream until it reaches the root. Once the root receives that TCN, it will begin sending configuration BPDUs out of all its ports. The TC flag is set on these BPDUs letting all switches in the topology know that a topology change has occurred. This is further described in the NetworkLessons note on the STP topology change process.
According to the official documentation, it is only when a switch receives the TC BPDU from the root that the aging timer for the MAC address table is reduced, and not when it receives a TCN from a downstream switch. The only exception is the switch on which the topology change was detected. In such a case, the age timer of the MAC address table on the originator of the TCN is immediately reduced.
So although SW1 sends a TCN and SW2 receives it, as shown in the debugs in the lesson, according to this, the age timer of the MAC address table of SW2 is likely not reduced. It is only when SW3 (the root) receives the TCN and sends out a TC BPDU that reaches SW2 that this will occur.
Note however, that the process from the point of view of SW3 is different. Normally, SW3 would try to send a TCN message out of its root port to reach the root bridge. Here, SW3 IS the root, so that isn’t really necessary. When this happens, because the root bridge itself detects the topology change, it will actually start sending out TC BPDUs on all its ports, thus it won’t actually wait for the TCN from SW1 to reach it.
If that is the case, that means that the topology is actually split into two sections that cannot communicate, or that have no link between them. If that happens then each section will indeed begin having an STP root election.
Please note that all of the above describe standard STP IEEE 802.1D. Remember, this version of STP is no longer used in production networks, however, its operation is good to know as a stepping stone to reach a good understanding of other types of STP.
I hope this has been helpful!