In regards initiating the Manhattan Project, Einstein and Szilard were clearly critical. Without them the entire project would, at a minimum, undoubtedly have started significantly later in the war. Szilard was the first in the U.S. to recognize the potential of an atomic bomb, and Einstein's celebrity, both in signing the letter and subsequently leveraging connections with the Belgian royal family to secure an audience with Roosevelt, ensured that action was prompt.
The letter is believed to be "arguably the key stimulus for the U.S. adoption of serious investigations into nuclear weapons on the eve of the U.S. entry into World War II". In addition to the letter, Einstein used his connections with the Belgian Royal Family and the Belgian queen mother to get access with a personal envoy to the White House's Oval Office. Some say that as a result of Einstein's letter and his meetings with Roosevelt, the US entered the "race" to develop the bomb, drawing on its "immense material, financial, and scientific resources" to initiate the Manhattan Project.
As for the project itself, Einstein's contribution was complete. He played no significant role in the project subsequent to its launch. That was far from true for Szilard. His energy and enthusiasm early in the project allowed him to solve problems that others had not yet even encountered, surely speeding up the entire project. Given the tight timeline at the end of the war in the Pacific, One could argue that his early contributions ensured completion of the bomb before an invasion of Japan had to be launched.
In November 1938, Szilard moved to New York City, [and] obtained permission from the head of the Physics Department at Columbia, George B. Pegram, to use a laboratory for three months. ...
Szilard and Zinn conducted a simple experiment on the seventh floor of Pupin Hall at Columbia, using a radium–beryllium source to bombard uranium with neutrons. ... they discovered significant neutron multiplication in natural uranium, proving that a chain reaction might be possible.
Szilard made another important discovery. He asked about impurities in graphite, and learned that it usually contained boron, a neutron absorber. He then had special boron-free graphite produced. Had he not done so, they might have concluded, as the German nuclear researchers did, that graphite was unsuitable for use as a neutron moderator. ... Fermi determined that a fissioning uranium atom produced 1.73 neutrons on average. It was enough, but a careful design was called for to minimize losses.
In January 1942, Szilard joined the Metallurgical Laboratory in Chicago as a research associate, and later the chief physicist. Alvin Weinberg noted that Szilard served as the project "gadfly", asking all the embarrassing questions. Szilard provided important insights. While uranium-238 did not fission readily with slow, moderated neutrons, it might still fission with the fast neutrons produced by fission. This effect was small but crucial. Szilard made suggestions that improved the uranium canning process, and worked with David Gurinsky and Ed Creutz on a method for recovering uranium from its salts.
[Szilard] was the co-holder, with Fermi, of the patent on the nuclear reactor. In the end he sold his patent to the government for reimbursement of his expenses, some $15,416, plus the standard $1 fee.
As for the "other scientists" aspect of the question: The Manhattan Project was a massive effort by thousands of scientists, engineers, human computers, and others. No one of these was absolutely critical to success - that's not how science works - but many in their turn provided critical insights and discoveries that had eluded others to that point. All of these led to faster success. The cumulative effort of all these individuals resulted in both the success of the project, and the timing of being completed as soon as it was.