People in my current industry (healthcare/biotech) often use the terminology "a software" and "these softwares." It irked me at first but eventually I got used to it.

I think it's because every piece of validated software that our company uses, however small, is assigned a unique number (e.g. "SW12345"). They're not all full-blown applications, so we can't call them that. Sometimes they're tiny programs or even just scripts.

Anyway, it's possible the person that wrote this has a background in a similar industry.

Is it an application?

yes. calling it "a application" is imho a lot worse than using "a software"

I'm pretty sure the ellipsis replaces another word... "a productivity application" or whatever

Isn’t it? I would call it a web app.