Triathlon bikes are about one thing, and one thing only. Aerodynamics. Dan Empfield, the creator of the Quintana Roo brand, recognized this early on. Cervelo came along soon after, and their designs basically changed how time trial bikes are viewed, with their breakthrough design of the P3 in 2001 (Company history here.)
This P3 design evolved, and there are a few models such as your pictured Giant that have completely vertical seatposts. Many other bikes don't have this, but do approach vertical, as the frame geometry is completely different than a road bike with the purpose of allowing a rider to ride more forward on the bike, bent over with arms in the aerobars. You will also see much different clothing (esp for road racers) as time trial suits are also designed with aerodynamic considerations.
Time trial fit is very much a science as well as an art form. These include the F.I.S.T. method (Also developed by Dan Empfield), Retul, which are two of the most popular, but there are a couple others as well. They look at such things as upper body angle, hip angle, leg angles at top dead center and bottom dead center (TDC, BDC), forearm to bike angles, etc etc. A very minor change in seat position can have profound effects on aerodynamics, comfort and power.
You will also see some different frames and components in the triathlon world than you will in the road race world, because as always, the UCI (governing body for cycling) has very strict rules for time trial bikes and components, and some of the items used in triathlons are not allowed for road time trial events. For example, Cervelo's latest model, the P5, has two different forks, one which is legal and one which is not.