Territory control is only a side effect of most wars. Most of the time, territory is gained for resources or to take away resources. There are other resources to take away or gain that are not geographically based - clear threat to financial stability is a simplistic example. That will certainly, through force, have the other side closer to suing for peace.
Air only (or officially air only) wars are a great counter example. You're not really taking territory, but controlling it. Why are you controlling it? To influence the enemy: Deny them freedom to move, to cause casualties, to damage production capability, etc, etc, etc in order to achieve a political objective. All of those are accomplishable almost exclusively in the cyber domain for some set of possible objectives.
Choosing to define something out of existence by using a purist definition defies how things work. More often, domains and tactics are blended together (air, sea, land, space, cyber) to achieve, by force, political objectives. Sabotage is part of war, as is espionage, as is subversion.
If the point was "there are no cyber-only wars", I don't believe it, but it's tenable (as is "there are no air only wars" - there is always ground support and/or ground effect). But that's not what the point of "carrot for those selling the stick" is. Whatever your definition of "war" is, several facts remain:
You can achieve kinetic, financial, and political effect using cyber only means; There is activity by nation states to use force in the cyber domain; Military organizations have already used cyber attacks in kinetic conflicts to help them achieve their aims against other military organizations.
You don't have to call any of these (or the sum of their implied possibilities) "cyberwar", but that doesn't mean the threats, vulnerabilities, or consequences are being hyped up either.