You're probably using a very old MySQL version (before 5.5.3). You need to contact your hosting provider and request an upgrade to the latest sub-version in 5.5.

If this is not possible, do the following:
- Download K2 from its GitHub repo: github.com/getk2/k2/archive/master.zip
- Extract that zip file. It will create a "k2-master" folder and in that folder edit the file administrator/components/com_k2/install.mysql.sql replacing all "utf8mb4" instances with "utf8".
- Re-zip the CONTENTS of the "k2-master" folder and upload to your site for installation.

What's your MySQL version?

If you can have PHP 7.2, you can clearly update to MySQL 5.6 or 5.7. If MySQL is stuck on 5.1 because of the OS's repos, then use MySQL's official repo which is a much better option either way.

Every other solution would be a hack...

If you check Joomla's technical requirements for MySQL you'll see that the recommended version is 5.5.x either way: downloads.joomla.org/technical-requirements

True dat :)