They are probably referring to the regulations and tax code at that time. America had (at one point) a 93% effective tax rate on the richest people. That is now less than 20% (if I recall correctly). Regulations also were less in favor of corporations and more in favor of people. That has flipped.

A combination of several things. Tax rates that encouraged reinvestment into businesses through higher pay and R&D. Stronger or more heavily enforced anti-trust laws that meant tens of thousands of more middle management, board and CEO positions across the country per capita. Stronger unions were more able to use collective bargaining for better working conditions, though there power and ability was already falling due to the red scare.

Obviously there were also plenty of problems then as well. So there shouldn't be a 1-1 return. The US population has basically doubled since the mid 1950's, which few seems to mention regarding the current housing situation. The auto industry was busy ruining mass transit across the country, or already had. The red scare hurt unions. Racism has always been a problem for people who didn't win the genetic lottery of their generation.

In reference to OPs question, it was not a guilded age. There was one before, and we're in one now. That suggests that the pendulum needs to swing back towards that direction. Depending on how things go in the near future it could slow the swing towards guilded (if labor actually starts winning) or not (if children are made to be workers, women to be only mothers and the Biden admin blocks the teamsters like they did the rail strike). Our constitution is fairly explicit about how government should run, but is rather quiet about the economy. The people need policies that works for the people, and they will determine that.

Apologies for using generalities, but it's a random thread on the internet. It's not a great use of time to get into fine details, especially when late to a post, unless it gains interest.