You contracted with a client for a $xxx,xxx project or engagement. You could go on to summarize the project--e.g., "to improve its marketing strategy" or "to update its payroll system." You could go on to say that you "successfully competed with other firms to win the contract."
The web site to which you refer is, I believe, using the words "sell" and "buy," which it often places in quotation marks, as metaphors: a project manager needs to persuade a client or a boss to undertake a project. Unless it's typical in your field, "selling a project" may be inappropriate, more characteristic of real estate than consulting.

You can use the phrase "sold a project" to mean that you convinced a potential client to start a project with your firm, provided the context doesn't preclude that interpretation. On the proviso: if, for example, the project was a property development and you were a real estate agent, you may need to clarify whether you sold a property or whether you sold the idea of developing the project.

There are at least a couple ways of looking at this.

1. Sell = persuade

Sell verb 2 Persuade someone of the merits of. ‘he sold the idea of making a film about Tchaikovsky’ - ODO

In this case, what you've done is to persuade the client that it would be a good idea to start a project with your firm. You've 'sold the project', and the next phase might be to negotiate terms and conditions (or the negotiations might have formed part of the persuading). The words "the project" is a metonym for the idea of launching said project.

2. Project = product

Sell verb 1 Give or hand over (something) in exchange for money. ‘the family business had been sold off’ - ODO

In this case, what you're a sales person, and you have convinced the client to sign up to undertake the project itself, not just that it's a good idea. Here, selling a project takes on the same feel as selling a tangible product. What you've actually 'sold' are the services of your firm.

Wanna know how to better sell your service? Package and position it like a product--these marketing experts show you how. - entrepreneur.com