Wherever you work in the USA there's a note in the employee handbook saying that the company may monitor any communications using company equipment for any business purpose, which is completely consistent with that ruling (and, even if it applied in the us, would render it moot).
No, "we may monitor your communication for any business purpose" would not be consistent with that ruling. There's no chance "any business purpose" would qualify as a legitimate reason for monitoring communications.
From the PDF press release linked on the COE site:
"The national courts [have not] carried out a sufficient assessment of whether there had been legitimate reasons to justify monitoring Mr Bărbulescu’s ommunications."
"Neither of the national courts had sufficiently examined whether the aim pursued by the employer could have been achieved by less intrusive methods than accessing the contents of Mr Bărbulescu’s communications."
In other words: You need a legitimate reason for accessing your employees' communication and you need to consider less intrusive ways of achieving your aim first.
So your boss is not allowed to just read your mail whenever he likes. Or maybe he is, if you're working in the US. But European courts, especially the international ones, are very strict about privacy and protecting personal rights.