This is the order in which it appears on the website:
Recent Bachelor's Degree Recipients
Graduate Students (1st year, 2nd year, 3rd year)
Recent Master's Degree Recipients
Pre-Doctoral Students (1st year, 2nd year)
I think they are referring to "graduate students" as recent bachelor's degree recipients and "pre-doctoral students" as recent master's degree recipients. So if you started your Ph.D. straight out of a bachelor's degree program, you are still eligible in your third year (as far as I know). This seems to disagree with the "Eligible applications are enrolled ... through the second year of a traditional PhD program" statement farther up on the page, but it has been the rule for the last few years.
From the old NDSEG facebook page (posted in 2011):
"According to the NDSEG Eligibility Guidelines, students are no longer eligible for the program if they have completed more than two years of full-time graduate study. If a potential applicant has just begun their third year of graduate study this fall then they are considered eligible pending they meet all other eligibility criteria."
From last year's solicitation:
"Students can start applying to the program as early as their undergraduate senior year and as late as the start of their third year of overall graduate study."