This summary is not the rule. The rule text controls.
Lawyers can't agree to limit their own right to practice law in the future, even if they want to. This means law firms can't make partners or employees sign contracts that say "if you leave this firm, you can't practice law in this area" or "you can't compete with us for a certain number of years." The only exception is for retirement agreements, which can include reasonable limits since the lawyer is stepping away from practice anyway.
This rule also applies when settling a lawsuit. If a lawyer is representing a client in a legal dispute, the settlement can't include a term that stops the other side's lawyer from taking similar cases in the future. For example, a company being sued can't offer extra settlement money in exchange for the client's lawyer agreeing never to sue that company again.
The reason for this rule is simple. Clients need to be able to choose their own lawyer, and lawyers need to stay free to represent whoever needs help. If firms could lock up lawyers with non-compete deals, or if settlements could push good lawyers out of certain kinds of cases, it would end up limiting choices for future clients. This rule keeps the legal system open so people can find the lawyer who's right for them.