This has been an argument not just made about tech but also other sectors, usually with a nationalist bend, for example Mexican immigrants taking industrial jobs from domestic minorities, and so on.
Many things wrong with this (including an odd definition of diversity that excludes nationality, culture, language and so on), but I'd want to stress one thing in particular.
In contrast to ivy league college admissions, the private sector is not a zero sum game. It is not a game of musical chairs. Immigrants coming to join any given economy aren't just occupying jobs, they're creating new jobs, both indirectly and directly. Indirectly of course by contributing to the overall wealth by creating value and creating demand, but also disproportionately(!) by becoming entrepreneurs.
The rate of entrepreneurship among immigrants particularly in the US is very high. A significant amount of the companies providing the jobs that Mr Jackson is talking about have been created, or are being led by immigrant executives or founders.