If the ownership did change, how was the player account details transferred?
Control of the game servers were moved to MegaDice
This is a blatant lie! Rakki N.V. was operator of satoshidice.com and had control of the game servers and Rakki N.V. is as well the operator of megadice.com and still has control of the same game servers.
How was the invested funds managed? Why were they not made known to players and investors?
An email was sent to all players and bankroll backers notifying them all satoshidice accounts were moving to megadice.com
Absolute nonsense!
If MegaDice is a separate entity (as you claim), there is a new contract relationship! You would need to
ask all players and bankroll backers if they agree to move their balance to the new entity MegaDice. As MegaDice is a new contract partner, all players and bankroll backers would also need to agree to your terms and conditions!
Only if MegaDice and SatoshiDice is the same entity, if the contract relationship did not change, then notifying would have been sufficient.
Reason why I am not believing most of this is because of the same public key as used before with Satoshidice. It really makes no sense to re-use the same key, especially with some many BTC at stake here.