Small correction: Gate's mom was on the board of the United Way, along with the (then) CEO of IBM. She convinced the IBM CEO to give Bill's fledgling company exclusive rights to DOS.
Even if MS had been licensed the DOS rights, if IBM had licensed the rights to MS and X other companies, the entire computing landscape would be totally different today, as well as other huge parts of the ecomomy (healthcare comes to mind...) would be totally different. WordPerfect would probably still be around, as well as Netscape. Bill would still be fabulously wealthy, but worth several billion instead of several hundred. I could go on for hours.