Why "Search apps", "Search files", etc. in software UIs, instead of "Search for ~"?

Search here means "search in", not "search for". A more long-winded version would be "search within the apps for the thing you want" or "search within the files for the things you want".

Now, when you search within the apps, you are actually searching for an app, but that doesn't mean that "search apps" is a shortened version of "search for apps".

First it should be said that the principles underlying the design of computer interfaces (called HCI in Britain) put a greater weight on clear and simple communication than on grammar. And rightly so.

It is easier to process the information in a button labelled “Close” than one with “Close + object” e.g. “Close this window”. (And one should avoid superfluities like “Please close” or “Close!”)

Another grammatical component that can often be dispensed with is the article (loud cheers from East of the Urals), as I think may be the case here.

“Search Apps” can be construed as “Search the Apps” i.e. “Search the section of our database that contains a list of apps”. (Not, I think, “search for apps).

(Search + article + noun) is fine grammatically, e.g. “The police searched the house.” (They may have also been searching for something, but that’s another story.)

So “Search Apps” is clear and much to be preferred to using an article, assuming that the context is also clear. If, as another answer assumes, it means “Search for Apps”, dropping the preposition may be more moot.