Adding HTML Code to Replace Text in PHP

One way to handle this with the approach you’ve taken is to expand on the PHP code for the check to see if the user is logged in like so:

<?php if (!is_user_logged_in()) : ?>
<style>
  .product-purchase-box{display: none;}
  .linktologin{display: inline;}
</style>
<?php else : ?>
<style>
  .product-purchase-box{display: inline;}
  .linktologin{display: none;}
</style>
<?php endif; ?>

Then, remove the HTML code for the login link within the <script> tags and add it to where you have the button HTML with the class .linktologin (or whatever you chose). Something like this:

<div class="cart-box row product-purchase-box" style="user-select: auto;">
  <div class="col-md-12 paading-left-0 product-price" style="user-select: auto;">
    <h3 style="user-select: auto;"><span class="edd_price" id="edd_price_4701" style="user-select: auto;">$0.00</span></h3>
  </div>
  <div class="product_widget_inside" style="user-select: auto;"> <a href="#" class="edd-free-downloads-direct-download-link button white edd-submit" data-download-id="4701" style="user-select: auto;">Download</a></div>
</div>
<div class="linktologin">
  <a href="https://ezcliparts.com/login">LOGIN</a> OR <a href="https://ezcliparts.com/register">REGISTER</a> FOR FREE TO ACCESS THIS AND ALL 1 MILLION+ DESIGNS
</div>