"Competing with" doesn't sound promising for the good of the game, any chance one or both of the other parties are bluffing for a piece of the action & will end up "working with" PRO for the greater good? Or is that just too in-American to hope for?
ProRugby's ace in the hole is their USA and World Rugby sanctioning. Which while not essential makes life a lot easier. A lot still has to go right for these other two groups to be even to the stage of announcing anything. I suspect one might be United World Sports (the group that runs the Las Vegas leg of the 7s World Series) and their Super 7s concept. Basically think 7s played over an hour time period using 12 min quarters and unlimited interchange.
Another possibility might be American Rugby Sevens. They ran a proof of concept 7s event last year that involved both the wider US and Canada 7s squads plus argentina and a couple of elite Olympic Development Academy squads.
Nothing has been seen from either in a while but that's not to say its not possible.
In terms of 15s. The American Rugby Championship concept developed by Moore Sports (was featured on The Rugby Club. They also organised the MLB games in Sydney) may be a possibility. RugbyLaw and the NRFL are essentially out of the running at present.
I think apart from the sanctioning agreement stating they had to get something up in 2016, the possibility of other competitors emerging is driving ProRugby. I'd still say these other groups have a less than 50% chance of getting anywhere.
The general consensus in the States is that multiple competitors is a positive thing. That it will end in a single unified league emerging. We'll have to wait and see.