The system was a based on a military messaging system.
What is important to note is before SABRE the system used was a sell at will until a stop message was issued. Then sales would be on request. This method is still used between different airline systems today.
Before the implementation of SABRE airlines used teleprinters as a way of communicating. Some of the commands SABRE and other IBM 360 systems come directly from this period. For example AJFkSFO9MAR was a way of economizing on characters sent. It means what is the available seats from JFK to San Francisco on the 9th of March. This predates SABRE.
There is several reasons that the System 360 (the reservation systems used by airlines like SABRE) is one that it is written in Assembler, and also the logic is very tied into its role of reservation. For example it was designed in the days of punchcards, which have a totally different method of matching than a relational Database. The logic is still used on matching a seat to a fare.
On the pure speed much of it is gained by clever engineering tricks. An example would be the passenger record. This is 9 alphanumeric id of the passenger reservation. It is the hash of virtual memory location of the reservation. It takes 4 cpu cycles to retrieve it.
The classic "the decision makers can take longer to buy than you can stay solvent" problem of enterprise sales.