I saw these specifications listed for a compressed air dryer (desiccant type). I also wonder, can we extract moisture without make it liquid (dew) first when in it is in a vapor state? How would we do this?
Start with the phase diagram of water found at this link. The solid <-> vapor transformation occurs at pressures below 1 bar. Using a temperature of -40 $^o$C puts the pressure around 7 Pa. This is vacuum conditions.
Unlike all five other transformations (e.g. fusion is solid -> liquid), the vapor -> solid transformation has no standard definition. In some cases, it is called solid-state condensation. In others, it is simply called vapor deposition.
The better term for the transition vapor -> solid is the frost point. However, the use of the word dew point is a hypothetical approach. It says that, when you would try to cool the air to saturate it with water, you must cool to that temperature. Yes, in this case, when you would cool an infinitesimal amount just below that temperature, you would create solid ice.
Finally, you can use a desiccant to extract water vapor from air without going through a liquid state. The water vapor adsorbs on to the solid.