Call of Duty: Black Ops 4 may be lacking in the single player campaign, but it looks like there will at least be savings for you on the storage front— according to the listing for the game on the Xbox Store, the file size for Black Ops 4 comes in at 42.64GB. This is actually roughly the same as Black Ops 3, which came in at about 45GB in 2015, but is far smaller than the 80GB that last year’s WW2 demanded.
The truly interesting thing here is that the store page simultaneously lists the game as being Xbox One X enhanced, so apparently, the file size calculated here is after accounting for the higher resolution (and therefore far larger) assets that that would entail. It seems like cutting out the campaign might truly have helped in saving on the file size for the game then.
The pre-load for the game is not currently available on any system, and the final file size may yet be different. Call of Duty: Black Ops 4 launches October 12 for PS4, Xbox One, and PC.