The MyCloud has the Twonky DLNA Media Server installed. This is a DLNA-compliant server, so any DLNA-compliant client device should be able to connect to it.
However, as larryg0 suggests, the ability to play media files depends on the client supporting the media format (both container format and CODEC format: google these terms if you’re not familiar with them). You can usually download manuals for any DVD player you might consider buying. These manuals will usually have a table of media formats they support via DLNA.
For an alternative approach that doesn’t rely on a ‘walled garden’ for the ‘smart’ functions, have a look at this thread:
Of course, if you’re looking to get a Blu-Ray player anyway…
