Ahhh, it's probably just a phrasing thing in the title. Temperature is just an accepted arbitrary value (25C) in this case, so we can measure the free energy in a "standard" state, as a reference point. So I guess it's standard state in the case of pressure and concentration. From my understanding, I think it's still considered "standard state" even if we fluctuate temperature, BUT we have to keep both temperature and atmosphere constant. It makes sense to me because deltaG is a state function and measures max amount of work in a system. That's why we have accepted deltaG for certain reactions and know if it's spontaneous or no.
Wiki says for standard state, "Strictly speaking, temperature is not part of the definition of a standard state. For example, as discussed below, the standard state of a gas is conventionally chosen to be unit pressure (usually in bar)
ideal gas, regardless of the temperature. However, most tables of thermodynamic quantities are compiled at specific temperatures, most commonly 298.15 K (25.00 °C; 77.00 °F) or, somewhat less commonly, 273.15 K (0.00 °C; 32.00 °F)."
Other sources seems to support the above too, so looks like the pressure is what's standard state?