The bed must be secured in some way: triangulation, gussetting, or rigid wall mounting. THIS IS IMPERATIVE
Can you see how the curved ply side panel edges actively provide rigidity by passing around the top panel intersections? Something of this ilk will be mandatory for any free-standing platform bed structure.
Without, the whole assembly will rack, the joints will fail, and the whole kit & caboodle collapse. The Canadian bunk bed you've linked is a tiny single children's bed. The dimensions & design ARE undoubtedly adequate for purpose, but not for your intended size & use!
19mm ply is insufficient to use as a base alone. You'll need at least a top-to-bottom (i.e. foot-to-head) 150 x 32mm reinforcing beam down the middle underside to prevent sag. You can't just "scale up" others' designs without compensating for the additional stresses of the larger structure & spans, which increase exponentially as a logarithmic rather than direct function of increase.
A wider &/or longer structure than that depicted must be heavily reinforced, triangulated and significantly over-engineered to allow for the extreme stresses induced by any anticipated activity. A bedroom mazurka for two, a threesome, pillow fights by children etc.
Any base material, either ply or slats, must be well perforated to allow adequate ventilation of the mattress base to prevent condensation and moulds developing.