Why doesn't temperature affect Pressure Altitude?
The picture you have displayed is correct. But, your understanding of what it is saying is incorrect. The picture is explaining the reason your Indicated Altitude will change with temperature for the same True Altitude. And, your True Altitude will change with temperature (a potentially dangerous situation) for the same given Indicated Altitude.
Your misunderstanding may stem from the fact that the Indicated Altitudes and the field level barometric pressure (or at least the Altimeter Kollsman Window) setting are the same in all three temperature scenarios. This is not the case for the pressure at 10,000 feet MSL True Altitude. The atmospheric static pressure at altitude for the three scenarios is not given. And, they can not be equal to 29.92.
The static atmospheric pressure is higher for the cold scenario and lower for the warm scenario at 100,000 feet MSL True Altitude. You would think that this would be the opposite way around. And, it is for air confined in a container. But, not for unconfined air or air confined in different sized containers.
Atmospheric air will become less dense and rise when warmed. This will create a partial void of air below it. This partial void is an area of low pressure since the surrounding air has yet to move in to fully replace the vacating air. If the air were to be cooled, it would sink onto the air below it. This would create an area of high pressure as the existing air has not moved outward in sufficient quantity yet.
How does this affect the different types of Altitude? Like this:

True Altitude is the height above MSL measured in actual feet of distance.
Pressure is just a measurement of the amount of air interacting with the measurement device and the average amount of energy each air particle has. Temperature will affect the amount of energy possessed by each air particle proportionately. This will either cause the  pressure to change proportionately. Or, it will cause the volume and density of the air parcel to change proportionately.
Barometric Pressure (Altimeter Setting, Kollsman Window Setting) is just the static atmospheric pressure at field elevation adjusted to show what the pressure should be at Mean Sea Level.
Indicated Altitude is just the reading you receive from your Altimeter. Your altimeter is just a very accurate pressure gauge (a barometer) calibrated to show the height above a specific reference line of pressure. The pressure and density of air at lower altitudes are greater than they are at higher altitudes. This is due to the sheer weight of the air from above pushing down and compressing the air below. The amounts of changes of air pressure and air density are known. This is based on observationally, scientifically and mathematically derived formulae and estimations that are based on the International Standard Atmosphere. On an ISA day, that reference line is equal to the Mean Sea Level. That is not always convenient since the atmosphere is not always at standard pressure and temperature at Mean Sea Level. So, most altimeters can be adjusted to account for non-standard barometric pressure.
Pressure Altitude is just the height above the mathematically derived line representing where the International Standard Atmosphere pressure of 29.92 inches of Mercury should be felt. Pressure Altitude is the height in feet you would feel the same pressure on a non-standard day as you would on an ISA standard day in feet MSL.  If the atmospheric pressure at MSL (or the barometric pressure at field elevation) is not standard, the two beginning levels will not be in the same place. You would have to make an adjustment to the height of MSL to derive the Pressure Altitude.   The pressure of air is derived from its volume and energy content. Temperature is a factor in this only if the air is confined or in a container.
Density Altitude is just the height above the mathematically derived line representing where the International Standard Atmosphere density. Density Altitude is the height in MSL where you would feel the same density on a non-standard day as you would on an ISA standard day.   If the atmospheric density at MSL is not standard, the three beginning levels will not be in the same place. You would have to make an adjustment to the height of MSL to derive the Density Altitude.   The density of air is derived from its weight and volume. Both pressure and temperature are factors in this only if the air is unconfined or in a container.

You derive Density Altitude by adjusting Pressure Altitude by atmospheric temperature. You derive Pressure Altitude by adjusting the True Altitude by the atmospheric pressure. You have to have each to get the next.
Case in point. If the air were confined to nice, neat, little columns with defined and rigid lateral boundaries and adjustable vertical boundaries, the average pressure in each container would remain the same. The heights of each column would be different based on temperature. For extremely tall columns, the pressures at the bottoms would all be equal. And, the pressures at the top would all be equal. But, the rate at which the pressures would change with height would be different. Since Indicated Altitude is just another way to represent the static atmospheric pressure at altitude, the Indicated Altitude of 10,000 feet MSL would be at different True Altitudes based on temperature.