I'm a non-native speaker (actually from Russia) and for us the articles (a, an, the) came as a thing that we just have to adopt. We do not have not similar constructions in Russian. Menus I see in programs, and other short phrases related to computer user interfaces usually lack articles (for example Open Location and something like this). I'm wondering, does it look natural for a native English speaker or is it something one is getting used to?
This style of writing is not only used for computers. It is also used for short notes, newspaper headlines, road signs, and many store signs. I think it is done mostly for saving space, and English speakers are quite used to it. I believe that it was completely natural to use this style for computers when they came along.
There is a brief entry about this in the last paragraph of this Wikipedia article:
In contexts where concision is especially valued, such as headlines, signs, labels, and notes, articles are often omitted along with certain other function words. For example, rather than The mayor is attacked, a newspaper headline would say just Mayor attacked.