This is a difficult one to give a definitive answer. Birch ply is usually regarded as being safe for hamsters however it all comes down to what glue they’ve used on the Laserply website it says they use a resin glue so I would be a bit skeptical as the resin could be formaldehyde. You could always reach out to the company they might be able to tell exactly what resin is used to glue the plywood together and that may help determine the safety of the wood to use around hamsters.
A plywood that uses soy based adhesive are safe a brand who makes plywood from this Purebond here link to their website faq-
FAQ. Frequently Asked Questions | PureBond(R) Plywood.