Apparently "runs until May 31st, 2003" only refers to free trial-out installations, rather than to what you get when you use it to upgrade a registered version (e.g., an OEM version that comes with a burner). It could mean that the free demo version will expire on May 31 (I can't be sure, since I've never used demo versions of Nero).
What I'm quite sure about is that beta versions never appear on Ahead's site.
Further, new versions tend to appear at the beginning of each month.
Thus, if you already have a registered version, there is no need to worry about the latest update!