MSN Messenger played a similar cat-and-mouse game with AOL Instant Messenger long time ago. Unlike MSN Messenger which used this publicity to grow their own market share, I am not sure what's the end game for Beeper.
they could and so they did.
The release of Beeper Mini certainly gained publicity for Beeper Cloud, and I don't see why Beeper Mini would cause Beeper Cloud to go defunct.
[1] Beeper Cloud: https://www.beeper.com/cloud
[2] Beeper Mini: https://blog.beeper.com/p/introducing-beeper-mini-get-blue
I don't think their interested in replacing iMessage directly, if that's your question.