They can't, at least not only "winning the fork war", as I already explained above (see here). Having the most popular Bitcoin website (bitcoin.org) is a BIG asset if you want to be in control of the code that will be used by the majority of the users.
What "they" can do - and only that - is to pursue a common agenda with miners and Bitcoin companies, trying to force the developers to include certain changes like the 2x weight/blocksize increase.
I think, however, that an "extended NYA" or a "new NYA for a 4x blocksize" (for example) will be very hard to achieve, because the NYA was an exceptional compromise in a pretty critical situation, and some or even most of the companies that signed it were more interested in Segwit than in the 2MB fork. Segwit would very likely still not be "live" if it wasn't because of Segwit2x, as the BIP148 folks never got the majority of the nodes and hadn't much hashrate support.
There were some pools - mainly ViaBTC - that greatly helped BCash getting some hashrate and becoming a major altcoin. We don't know what exactly was Bitmain's stance, and that's also why I wrote "or tolerated". OK, maybe I should have written "some Segwit2x supporters".
In my opinion, this is a slow "domino effect". If they perceive Sw2x to have low support, and thus do things (assign "BTC" to the 1MB chain) that will result in even less support, then it will be increasingly harder for Segwit2x to become "the Bitcoin". Not impossible, but I consider it unlikely, and the last ViaBTC statement (that they, for now, do not support 2x) has strengthened my belief in that the 2x chain won't "win" the "fork battle".