Is it possible to connect the BeagleBoard-xM to a monitor that only has DisplayPort available?
Not that I aware of.
Why couldn't he just use one of these cables?
Per wikipedia (http://en.wikipedia.org/wiki/DisplayPort#Compatibility_with_HDMI.2C_DVI_and_VGA):
Dual-mode DisplayPort can directly emit single-link HDMI and DVI
signals using a simple passive adapter that adjusts for the lower
voltages required by DisplayPort. When dual-mode chipset detects that
a DVI or HDMI passive adapter is attached, it switches to DVI/HDMI
mode which uses the 4-lane main DisplayPort link and the AUX channel
link to transmit 3 TMDS signals, a clock signal and Display Data
I'm not 100% sure the necessary level shifting works the other way,
but the fact that people sell cables for it makes me think there is a
good chance (though that isn't a guarantee).
That one is vice-versa, DP laptop to HDMI on monitor.