Each TMC2208 circuitboard design utilizes a grid of built-in "vias" that are placed directly underneath the TMC2208 chip. These "vias" are essentially electrically-conductive "tubes", which, due to the fact that they are nearly always copper, are highly thermally conductive too. Thus, when the TMC2208 gets hot, the vias get hot too. Since the copper on both sides of the board is connected, the heat transfers over to the opposite side of the board, where convection cooling whisks away some of the heat buildup, This helps to cool down the TMC2208. But, only marginally more than simply leaving it alone.
However, it provides a rather nifty feature! By providing a highly thermally conductive channel on the opposite side of the board, a massive heatsink can be placed on the stepstick that can adhere to the circuitboard itself, on the opposite side of the one the chip resides on, cooling it off. However, heat is heat, and placing the heatsink directly on the chip -- even with the vias trying to pull some heat away -- will still act to cool it down. For the intents and purposes of 3D printing, the only real difference between on-chip heatsinking and on-circuitboard heatsinking is structural. On-chip can run the risk of bumping into the heatsink and damaging the chip. On-circuitboard runs a far lesser risk of this due to not being exposed to the chip. While it is true that there are more nuanced discussion points than that alone, you do not run into them sufficiently enough to waste time teaching about, it quickly leads to heavily diminished-to-zero returns.
So if you look at any Trinamic driver, flip the board upside-down, and see a square-ish pattern of subtle dots, your eyes are not fooling you, you are seeing the vias at work! Each dot is a via, and inside of each via is a strand of copper, akin to an embedded wire. Neat!