There is no indication on the packaging regarding this. Here's my take: The cups are stainless steel and the gap is a vacuum, so I can't see any reason not to wash the cups in a dishwasher. The lids are small and plastic. They're probably safe in the top rack, but there is the possibility that the spray might cause them to fall to the bottom of the washer and melt on the drying element. Drying heat might also degrade the seal over time. So I would wash the lids by hand.
These small tumblers did not include any instructions unfortunately but the similarly constructed 20oz Emperor Tumbler (15993) I have did and they recommend only hand washing. I have liked both so far, they keep liquids cold or hot for a long time.