Did Malairte hold an ICO or private sale?

No. Malairte was never funded by selling coins to the public or to insiders. There was no ICO, no IDO, no presale, no seed round, and no private allocation. Coins only ever came from mining. You can confirm this by reading the project documentation for any mention of a sale, by inspecting the early chain for mass distribution out of a sale wallet (which you will not find), and by reconciling circulating supply with what mining alone produces. A token sale would inject coins that mining cannot account for, and no such gap exists in Malairte's history.