Understanding what a Letter of Intent is and when to use them is a bit confusing. But basically, this letter just means you are serious about continuing towards a purchase and that you want the other party to stop entertaining other offers. Our Letter of Intent template is suitable for all states.
Also, her closing call to action sounds more like a threat. You want to leave the reader with an avenue for follow-up, but don't intimidate them into responding. After all, they're not obligated to respond. You want to make them want to reach out to you for more information or next steps.