The NYT correctly stated in the parent article, "Ms. Manning was still known as Bradley Manning when she deployed with her unit to Iraq in late 2009." See how that works? She was always a she, even though she was presenting as a man at the time.

Trans binary people enforce their gender identity quite strongly because they get so much "pushback" (a polite way of saying harassment and threats) from people. In this case "they" is tapping into that.

If you think this is complicated, try calling a baptist a catholic and see what happens.