Is it an inherent property of glass that it will not take a crystalline form, but remains amorphous instead? Glass consists mainly of silica, but other substances are added, whch have the effect of lowering the melting point.
Glass blowing is done by heating the glass up to a temperature where it glows red hot, at which point it is about as malleable as clay.
The glass blower takes the glass out of the oven and works on it for a minute or so. By then the class is no longer hot enough to work it and the glass is put back in the oven. This cycle is repeated as many times as it takes to create the product.
As far as I can tell glass blowers do not have to take any precaution against the glass crystallizing (which presumably would alter the properties of the glass). Never happens, it seems.

Comparison with metals:
With metals the rate of cooling down will in general make a lot of difference. A steel with a composition suitable for hardening is hardened by way of quenching
If a steel cools down slowly there is time for the atoms to form large areas of aligned structures. Generally: the larger these areas, the more ductile the metal.
Clearly these properties of metals are not applicable in the case of glass.

In the process of glass blowing the glass is heated to a red glow repeatedly. As far as I can tell from the videos of glass blowing I watched: there is no change of the properties of the glass. That raises the question: is it possible at all to make a glass that does crystallize upon cooling down slowly?
 A: The elements (sodium oxide and aluminum oxide) that are added to silica to make glass are called (surprise) glass formers. In addition to dropping the melt temperature, they disrupt the formation of a 3-D crystalline network of the silica units in the mix and thereby prevent the formation of long-range order (i.e., crystals) in the solid, within the time available for that to occur.
For nonmetallic glasses, the diffusion-driven time scales needed to assemble zones of long-range order within a matrix of disrupted material are so long that by the time the material has cooled enough to effectively stop this recrystallization process, no long-range order has formed at all and the solid is completely amorphic.
For metallic glasses (which are really coool things!) the cooling rate required to ensure that the glass formers (which in this case are metal atoms with significantly  bigger atomic radii than the bulk material) will successfully inhibit the crystallization kinetics are of order ~millions of degrees per second, which require special ultrahigh-speed quenching processes like splat cooling.
