The ground is to shield the case, just as you might want to ground the 'can' on any crystal.
Whether you need to add capacitors or not depends on the application. Some chips might have integrated capacitors that are close enough.
But in most cases you would have to calculate the appropriate load capacitors for the crystal and for your layout and add them externally, probably about 15pF for this particular crystal (specified as 10pF load capacitance) and a good layout.
It's up to you to provide that equivalent load capacitance for the crystal, otherwise you may not get a frequency that is within the guaranteed limits, or, in the extreme, the circuit may fail to oscillate at all. It may fail to oscillate or start anyway, but that's more of a system problem.
Things in the datasheet that are your responsibility: