Does it mean that we need to wait until the Artemine ICO ends for those tokens to be totally burned?
No. These tokens cannot be accessed (because of the empty smart contract) so cannot be burnt anymore. These tokens will remain there forever, but because these are still "alive", supply will not decrease, and this is the main problem.
...and this is the main problem.
What problem? The tokens are destroyed forever, they cannot be spent ever again.
That's what the concept of burning coins is, what is your problem?
Many other devs burn tokens or ETH by just sending them to the address
https://etherscan.io/address/0x0000000000000000000000000000000000000000 and they are not reduced from the overall supply, not even the ETH...
Even the bitcoins destroyed by Satoshi were destroyed by him just by deleting the private keys... and the bitcoins were never reduced from the overall supply, it doesn't really matter AT ALL
Those 568375 MNE are gone forever no matter what