Cross-platform compatibility means the software runs on more than one kind of device. In signage that specifically means the player: Samsung Tizen, LG webOS, Android, BrightSign, Windows and Linux boxes, each with different capabilities and different lifespans.
It matters because hardware decisions outlive software ones. A fleet bought over five years will contain several generations and probably several vendors, through mergers, discontinued lines, and whatever was available when a site opened. Software tied to one platform turns every hardware change into a migration.
The caveat is that "supports" covers a wide range. The same product may render a layout perfectly on one platform and drop animation, live data or multi-zone playback on another, because the underlying browser is years older. Support is a spectrum from "full parity" to "it launches", and the spec sheet does not distinguish them.
Test the layouts you actually intend to run on the oldest device in the estate. That device sets the real capability of the network, not the newest one in the demo.