This is the exact issue. The DOJ's Antitrust Criminal Enforcement Division breaks up the companies by making an argument that's then directly contradicted by the DOJ's Merger Enforcement Division's (very outdated) policy on approving mergers. From the Merger Enforcement Guidelines[1] (last updated in 1997):
> By definition, non-horizontal mergers involve firms that do not operate in the same market. It necessarily follows that such mergers produce no immediate change in the level of concentration in any relevant market as defined in Section 2 of these Guidelines.
The Merger Enforcement Division's assumption may have been true in 1997 but it's difficult to argue that simply because Google and Amazon don't operate in the "same market" as their primary businesses that their combination would "produce no immediate change in the level of concentration" of the market for both online advertising and computing services. Yet, under these guidelines, if a Google + Amazon merger were proposed it wouldn't present any immediate issue for the Antitrust Division to oppose it.
[1]https://www.justice.gov/atr/non-horizontal-merger-guidelines
