Jets are owned by TNSE, which is jointly owned by Chipman and Thompson. In terms of board seats, Thompson controls more than Chipman so he likely has a bigger stake. Chipman appears to be the face and sits on the board of governors, so he's the one that is "in charge" so to speak, but with board control, Thompson could more or less fire Chipman from his current position as Executive Chairman of the Winnipeg Jets if he wanted to.
With what looks like to be a rebuild coming, and the lack of corporate support due to Winnipeg's smaller business community, the Jets will likely be in for some lean years. As long as it remains a passion thing for Chipman with the backing of Thompson, I don't think a sell and relocate is on the table right now and TNSE may be OK eating losses on the whole thing.
The question becomes what happens down the line when Thompson passes and moves his holdings to his heirs, will they share the same passion for having a hockey team in Manitoba? What happens with Chipman at that point? As mentioned, the longer the Jets remain in Winnipeg the more firmly entrenched they are. More than likely a day will come where they will need a new Buyer, and at that point the question becomes if they can find one in Winnipeg.
The NHL isn't inclined to look for relocation, that's been the major trend of the last 20 years or so across North American sports leagues, but as we see with the Thrashers, Rams, Chargers, Raiders, Athletics... it's not a free ride forever. Winnipeg is nice in that it doesn't really cover off land that is covered by anybody's geographic area, so nobody is particularly inclined to want them out to capture that fanbase. On the other hand, as a small media market, any value that they add to the League's overall television deals in both U.S. and Canada is probably not going to be all that significant, and if an ownership group emerges with an arena ready in a larger media market, the NHL may not fight overly hard to find a new group in Winnipeg.
All of this appears to be a long ways away, as this report doesn't give any indication that Chipman's frustration with ticket sales is leading him to get cold feet over the whole prospect of continuing to own a team in Manitoba.