Oh, yes. I missed that this part was not described.
In this case, you need to add the following lines into the runBuildCacheHandler() function in the Main.php file.
Do not forget to rebuild the cache after that and this change should do the trick.
Code:
$layout->removeTemplateFromList(
'product/details/parts/common.button-continue.tpl',
'product.details.page.info.buttons.cart-buttons'
);
$layout->removeTemplateFromList(
'product/details/parts/common.button-continue.tpl',
'product.details.quicklook.info.buttons.cart-buttons'
);