People run technology. People have knowledge. These things die when people die.
The richest 1% are not those people. We'd have a better chance with a random selection (only 12% of billionaires are female!)
The internet, electricity, running water, sewage, do not work unless someone is operating and maintaining them. Manufacture of supplies to maintain them depend on coordination across the globe, and further specialized skills.
Effectively, technology will be reset for at least a generation to pre-electricity levels. This is survivable, sure.
But, the way I see it, if this event happened instantly or close to it (months, even) the survivors would not be prepared to shift immediately to that lifestyle. This is where I would predict mass deaths.
I've also been assuming these people are not together in one place, and without air travel they would be limited to a shorter range. I suppose if they were all smart enough, they might congregate in a few different places. There's a chance if they cooperate and don't fight each other. Humans can do that. The richest humans, though?
If they survive multiple generations, then they survive. I give that a less than 50% chance ("unlikely"). Selecting for the wealthiest 1% is selecting for 1) elderly 2) psychopathic 3) men. Only 10% of the population of the richest 1% is female, and I would assume they are also older than the average person. I'm putting a lot of weight on the psychology of the wealthy and the state that we've "collectively" (it was them) put this planet into.