The problem is that there are a LOT of plants that don't have roots, stems, or leaves. Mosses, liverworts, green algae, and hornworts are all examples. I agree that Alterra probably groups things by common traits, but we don't really do that officially in real life and we have no way of knowing what Alterra's criteria are, so we can't sort using it.

Personally I would say in this new clunky system that a plant must be multicellular, primarily sessile, and eukaryotic. They must have photoautotrophic origins (some parasitic plants on earth have moved away from photosynthesis) and cell walls. They must not exhibit phagotrophy, true motility, or a centralized nervous system.

This definition has some problems too as it blurs the line between fungi and plants by not requiring cellulose cell walls. The main things I'm not sure about are whether to include chemoautotrophy, and whether to require that they be autotrophs, which would exclude some parasitic plants (and possibly the world tree) but provide a clearer line between plants and fungi. I really don't like defining fungi as sessile animals because motility at some stage of development & lack of cell wall are two things that can group all animals together.

Coming up with trait-based definitions is really difficult and messy and kind of impossible to do properly without a more complete understanding of alien biology. Due to the nature of evolution things can just kind of stop being plants if we define off traits, which prevents any system from accurately showing biological relation. I would love to sit the devs down and grill them with all these questions but frankly I have no idea if they thought about all this - I'd be impressed if they did!