Incorrect resonator/crystal PCB layout?
Well the two GND pins are probably there to bring casing and everything to a defined potential; thus, performance will be better when you connect them, but it might work without. Hard to tell.
However, this connection (for the low frequency of 16 MHz) doesn't need to be crazy good – a short, well-soldered wire that connects the two ground pins to the nearest ground contact should work.
Generally, unless you're doing really high-frequency things, or more than 2 layers, if in doubt, have a ground plane. If you have one, finding a place where to solder these might be really easy (you can even scratch off a bit of solder mask, apply flux and solder directly onto that.)