I disagree strongly for the reasons I explained in the rest of my post.
Well, fundamentally we are just arguing over the definition of a slang term. However, I think your understanding of the term is divergent from how the term is commonly used and from how the term is intended.
'Murderhobo' as a term was intended to describe D&D as it was commonly and perhaps most commonly played. It was a term intended to describe the fact that regardless of the nominal alignment of the PC, what they actually did was wander from place to place killing things for money. This was because per the rules what you were rewarded for was killing things and taking their stuff. The PC's behaved that way because the motivation of the players was to 'win' under the terms set by the game.
A party that goes from place to place being hired out to kill whatever the latest problem of the day is a 'murderhobo' party, even if quite arguably there is a good and justifiable reason for killing the bandits, ghoul king, dragon or whatever and they are not even engaged in acts that are technically 'murder'. The term is intended to highlight that in general the reason for killing the thing tends to go by the wayside in the long run, and the thing is instead actually killed because it offers XP and treasure. There might be a color of heroic activity, but this color is generally a shallow means of blessing killing whatever it is and taking its stuff.
Mercenaries and murderhobos may share many things in common, but where they differentiate is that a muderhobo, like a muderer kills things on whimsy.
While that's an interesting concept, it has nothing to do with the term 'murderhobo'. Not all 'murderhobos' have evil alignment, where as certainly any PC that kills indiscriminately out of whimsy is in every edition of the game is evil aligned. Ironically, these serial killers you describe might not be 'murderhobos', but might in fact be participating in an evil campaign. Whimsy as a motivation, rather than acquisition of XP and loot, implies that at the metagame level, it's possible (though by no means certain) that the player has actually separated the nominal goal of play (leveling up) from the goals of his play and his character. If he's consciously playing his character in a way that involves something other than maximizing the safe acquisition of loot and XP, and instead is focused on exploring the mental space of his character or his character's relationship to society, you might have an evil campaign that features wandering murders but not murderhobos.
Mudering, thieving, violent business people but as much as a mercanary likes killing, they also like money. A murderhobo has no love for anything except killing.
That's exactly backwards. The problem with your definition is that as you define it, murderhobo is fundamentally a synonym for murderer. It doesn't describe any game culture artifact that is particular to the game of D&D. Murderhobo's are murderhobo's because the metagame of D&D rewards killing things and taking their stuff as the preeminent and easiest way to succeed. The nominal motivation of the character doesn't matter, because it is subordinated to the player's motivation of killing things and taking their stuff.
The term 'murderhobo' was invented because a term was needed to refers (usually) to nominal heroes, not nominal villains. We could just call villains villains without needing to invent a term.