Limits to use an off-the-shelf grounded AC-DC power supply with a two-prong cable
As is the case with many power bricks, this one has a floating output
whether or not you connect its ground.  The datasheet confirms it by
listing input to output isolation as 3000V.  That means you can connect
one output terminal to 3000V from input ground, current flowing in that
connection will be negligible, and the voltage between the + output and
the - output will still be 24V.
You can verify it by plugging it in and measuring resistance between an
output terminal and earth with a good multimeter, or by verifying that
it works with earth disconnected.
This property is useful when you want a negative voltage.  For example,
I recently made a device that required -5V supply and its ground had to
be connected to earth ground.  I used a regular USB power brick, its +5V
as the device's ground and its ground as the device's -5V.
All that said, I don't see a class I or class II appliance class
marking in the
datasheet.  Make sure that regulations allow its earth unconnected.