Caption: A log-log plot of escape velocities (probably from a reference surface radius) versus some reference temperature for representative Solar System objects showing lines above which the specified gases (labeled above the lines) undergo total??? atmospheric escape (down to some reference minimum level) since the Solar System formation (4.6 Gyr BP) ???. The Solar System objects are approximately to scale and the actual data points are the centered black dots (which can't always be seen).
In particular, total atmospheric escape requires specifying some time over which it is judged to happen. One can only guess here that the author means since Solar System formation (4.6 Gyr BP).
Of course, total atmospheric escape can happen over millions to billions of years depending on the astro-body's escape velocity and surface temperature. This is, of course, implied by the plot.
Note also yours truly thinks the results in the plot are from idealized calculations, and so are only approximate for the real Solar System objects in any case.
Howsoever, the plot shows the main trend: atmospheric escape increases from upper left to lower right: i.e., as astro-body's escape velocity ↓ and surface temperature ↑, atmospheric escape ↑.
The temperature for the Earth is probably the Earth mean surface temperature 287 K (1961--1990). The Venus temperature may be from somewhere high in the Venusian atmosphere (see Wikipedia: Atmosphere of Venus: Troposphere). It's NOT the surface temperature which is 740 K (see Wikipedia: Atmosphere of Venus). For Titan (which has its Titanian atmosphere), the temperature is the surface temperature.
The temperatures for the gas giants may be those at the 1 bar radiis.
Now atmospheric gases almost always have a Maxwell-Boltzmann (MB) distribution of velocities which formally only goes to zero at infinite velocity. So there is always a high-velocity tail to the MB distribution. The higher the temperature, the bigger the tail of molecules. So higher temperature in the upper atmosphere increases atmospheric escape.
Now the MB maximum velocity v=(2kT/m)**(1/2), where Boltzmann's constant k = 1.380 649*10**(-23) = (8.617333 262... )*10**(-5) eV/K (exact) ≅ 10**(-4) eV/K , T is temperature, and m is molecule mass. The high-velocity tail of the MB distribution is correlated with the MB maximum velocity.
So as T ↑, atmospheric escape ↑ and as m ↑, atmospheric escape ↓.
v_escape = sqrt(2GM/R) = (11.180 km/s) * sqrt[(M/M_⊕)/(R/R_eq_⊕)] ,where gravitational constant G = 6.67430(15)*10**(-11) (MKS units), M is the mass of the spherically symmetric astro-body, R is the radius of the spherically symmetric astro-body, and the 2nd version of the formula is written in terms of Earth units as indicated by the Earth symbol ⊕.
Now note that as M/R ↑, v_escape ↑, atmospheric escape ↓ since fewer molecule have the necessary escape velocity.