First, some definitions:
5.1 Shared by (two or more people or things)
‘The minibus will be shared between the two charities and is due to be handed over at the end of January 2005.’
1 From one side to the other of (a place, area, etc.)
‘Pieces of the aircraft were strewn across a vast area.’
Although sharing power between factions and sharing power across factions both have the idea of the factions sharing power, the sense is somewhat different.
There is the notion that between is used for only two parties, while among or across is used for more parties, but there is also a case for saying that differences between multiple parties is idiomatic, while positioning between multiple parties isn't. Have a look at this comment on ELU and the dictionary entry it cites (just before the thesaurus section). In any case, this is somewhat superficial.
The deeper nuance is that sharing something between groups has the idea of a cooperative sharing, while sharing something across groups suggests a competitive sharing. This comes from the idea that something placed between parties is accessible by every party (e.g. one party gets the whole car on weekdays, the other on weekends), while something strewn across parties is only available piecemeal by the parties (e.g. one party gets the steering wheel while another gets the engine).
In the context of political factions and power, talking about sharing power between factions suggests a friendly relationship. Talking about sharing power across factions suggests the splitting of the power base, perhaps into checks and balances, or financial vs judicial, or via some other method of apportionment.
Nevertheless, regardless of the relative merits of using between or across, your quote says that the President didn't share the power.