Thinner air, potentially, yes, but mostly, the power of the pump comes into play the higher the psi you are filling your tires to. The difference between 30psi and 40psi is significant to small pumps. You need to look at the pump's capabilities, like air flow @ 0 psi vs @ 30 psi, load at operating temperature and maximum pump pressure.
The CKMA12 is capable of 3.08 cfm @ 0 psi and 2.34 cfm @ 30 psi, with a 100 psi max. The duty cycle is 50% at room temp, 72° F - meaning it needs to rest as much as it operates, like use for 30 mins, rest for 30 mins - at hotter ambient temps it needs to rest more, at cooler temps, slightly less. The current draw in amps to operate at full load and duty cycle is 12.4 amps vs 7.1 amps at 0 psi.
The CKMTA12 (the dual pump) doubles those values and can tolerate no rest for double the time, achieving 150 psi max pressure, but also draws more than double the current load, maxing out at a 50.4 amp draw.
Temperature, altitude, load and duty cycle all come into play when considering a pump for the task.
I used it at "altitude" at the top of Cleghorn, north of 3,500' IIRC, and it took about the same time as at sea level. A pressure gauge that references the atmospheric pressure around it will read higher at altitude so always double check tire pressure at your usual elevation or compensate for that when airing up.
I live at sea level so I had to add a around 3 psi to each tire after the drive home.