You can call it IEEE-488.1 to be precise. The IEEE-488.1 standard covers the physical and electrical interface (Where the time has come to retire it).
IEEE-488.2 standard covers the command structure, number representation, line ending etc. and is far away from being obsolete. It is the basis for commands used when you have a LXI or USB TMC measurement device (toghether with SCPI).
When you buy USB based measurement equipment, try to use USB TMC devices. As with GPIB it makes your live easier in the future (simply because it is a multivendor standard).
"...The next logical step is embedding the measurement results into a web site and accessing them with a standard web browser."
Not understanding exactly how the question of survival of GPIB (IEEE-488) is dependent on this, as I have not used it in last 5-7 years but I completely agree...that remote monitoring is going to be the trend for measurement going forward and as mentioned. Also, the instruments would get more dependent on an external display rather than having an internal display.