Normally the plugin assigns the correct capabilities, but for whatever reason this didn’t work for you.
You can use any capability-editing plugin to assign the following to the admin user (or to the Administrator role):
publish_airdrops
edit_airdrops
edit_others_airdrops
delete_airdrops
delete_others_airdrops
read_private_airdrops
edit_airdrop
delete_airdrop
read_airdrop