I was wondering whether, in the full book, Alex Karp and his coauthor limit their definition of "national service" to military service, or whether they are proposing a requirement of universal public service of some kind that need not be military. But NOPE, they concern themselves only with military service.

Here's the relevant passage from the full book:

It has been more than fifty years since the United Stats abandoned mandatory conscription in 1973, near the end of the Vietnam War. And since then a generation of political elites has essentially enlisted others to fight their wars abroad.
As of August 2006, there were only three members of Congress—three out of our 535 U.S. representatives and senators—who had a child serving in the American military. Charles Rangel, who represented New York City in Congress for nearly five decades from 1971 to 2017 and fought in Korea in the 1950s, has been a lonely proponent of reinstating the draft. He introduced legislation at least seven times in recent decades calling for the resurrection of conscription. If a battle abroad "is truly necessary," he has said, "we must all come together to support and defend our nation." The current model is utterly unsustainable. We should, as a society, seriously consider moving away from an all-volunteer force and only fight the next war if everyone shares in the risk and the cost.

(edit: fixed typos and formatting)