You might be able to get it work if you choose the following settings:
When exporting, choose View > Actual Size and Layout > Single Page.
But you'll have to change the way Adobe Acrobat or Reader display the PDF. I believe InDesign assumes that Actual Size will be viewed at 72 ppi. Acrobat/Reader calculates resolution in a different way. On my Mac Book Pro, Acrobat showed my system resolution to be 110 ppi. Therefore, In Acrobat/Reader Preferences > Page Display > Resolution > Custom Resolution : 72 ppi.
But each PDF reader will probably display it differently.
Interesting, if I set my to custom to 72 pixels/inch it fits exactly. I do not understand it, my monitor is 24inch and the custom default in PDF is 110 while the system is 96.
What I fail to understand is that I selected intent = Digital Publishing. When you create such a document you enter the size in pixels. On a 1920x1080 pixels screen it should fully cover the screen regardless of pixels/inch. Right?
Note: the first posting has a typo not 1280 but 1080.
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PDF pages are always measured in physical units (points, or 1/72 of an inch). There is no concept of a page being measured in pixels.
When you create screen-mode files in ID, it simply uses 72PPI and creates an inch-based layout. Look at the properties of the PDF file and you'll see the actual 'paper' size.
If you set the PDF's properties to open in full-screen mode, and the aspect ratio matches the user's monitor, then it will fill the screen perfectly - but all other modes it will be at the mercy of the user's display settings and hardware, because Acrobat/Reader is trying to show "100%" in inches, not in pixels.