$300k for a top executive position isn't especially high for anywhere in the US. That's around what the administrative director of a hospital would be making, which seems like a much smaller scope than leading ArXiv. For comparison, my roommate works for a non-profit that serves Philadelphia whose CEO's salary is $1.1 million. The CEO of the wikimedia foundation, which is similar in terms of role, has a salary of $450k. General average for US CEOs including for profits is around $800k and for large organizations tens of millions is not atypical.

Non-profits aren't maximizing stock value, but they do need to optimize for stakeholder value - you want to maximize the amount of money being donated in and you want to make the most of the donations you receive, both to advance the primary mission of the non-profit and to instill confidence in donors. This demands competent leadership. The idea that just because something is not being done for profit means the value of the person's contributions is worth less is absurd. So long as the CEO provides more than $300k of value by leading the organization, which might include access to their personal connections, then the salary is sensible.