Everyone becomes aware of words and phrases at different times, depending on their age, education and exposure. Just because you first widely heard of something at a certain time, does not mean it did not exist before that.
My older brother was an intern mainframe programmer in the mid 1960s. The use of "computer application" dates from at least the early 1960s, and can be found in books from that time.
(I read everything about computers back then, and even collected magazine pictures of them. Like many kids of the time, I got my first Edmund Scientific 3-pot analog computer in 1962, and a plastic
3-bit computer kit in 1963. In 1964 I homebrewed my first handheld analog calculator.)
The reason we don't find the use of the abbreviation "app" in the literature from back then, is that society was more cultured and formal, and did not use a lot of slang when writing for publication.
However, anyone who used the word "application" a lot, tended to use "app" in speech to save time amongst peers. With others, you used the full word so as not to leave them out of the conversation.
But not always. Sometimes the abbreviation worked. "Killer app" is an example. As for mobile devices, using "app" instead of "application" was appropriate because it was smaller, like the screen sizes at the time.
Certainly by 2000, "app" was being widely used in handheld device articles.
