The solution mentioned below is the method I used to convert our website to OpenMage.
Because I can't stress this enough:
Make a backup
First try on a staging environment
As from your question it's not apparent whether you installed the system via composer or just by downloading the files, the way you phrased it leads me to think you used the latter method.
The guide first says that it's good if you update to the latest Magento 1 version currenctly 126.96.36.199. I would suggest you follow the default magento procedure for updating which works most of the time.
I've been using this quick reference for ages without issues
Let's upgrade to Magento 188.8.131.52
Tools used in this part:
cd <root magento installation directory>
chmod +x mage
php downloader/mage.php mage-setup .
php downloader/mage.php sync --force
php downloader/mage.php install http://connect20.magentocommerce.com/community Mage_All_Latest --force
rm -rf var/cache/* var/session/* var/locks/* var/full_page_cache/* tmp/*
rm -rf downloader/pearlib/cache/* downloader/pearlib/download/*
chmod +x mage
php shell/indexer.php reindexall
php downloader/mage.php upgrade-all --force
You should have magento 184.108.40.206 now.
Let's install OpenMage
For installing OpenMage it's best if you learn a bit about composer first and how to integrate with magento.
The tools we're using for this are
composer require --no-update magento-hackathon/magento-composer-installer #="3.2.*"
composer update --no-plugins --no-scripts magento-hackathon/magento-composer-installer
composer require aydin-hassan/magento-core-composer-installer #~1.2
In order for these to work we need to setup some configuration options
composer config extra.magento-deploystrategy "copy"
composer config extra.magento-force "true"
composer config extra.magento-core-package-type "magento-source"
These config options will tell composer how to install the files for modules and the core.
Finally you need to install the openmage core
composer require openmage/magento-lts #~220.127.116.11