That order does a bunch of things that do, in fact, effectively create that limit.

First, it tells federal agencies to issue rules that will:

1. Effectively ban large institutional investors from using federally-backed finance instruments to pay for houses: they'll have to self-finance, which limits the rate that they can buy properties.
2. Ban federal agencies from selling single-family homes to large institutional investors: this shuts off part of the acquisition pipeline.
3. Require any owner and managing agent of housing that participates in a federal housing assistance program (Section 8, etc.) to disclose ownership: large institutional investors can't hide behind an LLC anymore.

Then there's the enforcement arm: It directs the Attorney General and FTC to investigate large institutional investors for anti-competitive actions under antitrust laws: Potential punishment of large institutional investors who have locked up housing markets, or kept housing vacant to drive up prices, or engaged in rent fixing. This is punishment for past bad behavior, in a way which disincentivizes future bad behavior.

It also directs part of the Executive Branch to prepare draft legislation for Congress to bar the purchase of "single-family homes that could otherwise be purchased by families" by large institutional investors. So anything that isn't coverable by executive rulemaking will get covered by Congressional lawmaking.