Nick here from Shopify. Great question!
I looked into this for you and checked with our themes support team to be sure. It seems like the example store you are displaying which has the icons must be on the Shopify Plus plan to be able to display the icons/ edit their checkout.
Even being on plus, this store owner would have to have modified the Additional Script at checkout, which is something Shopify doesn't support. You can also read more about the checkout.liquid file in the Shopify admin here.
The only other thing I could think of which would enable this to be shown is an app because of the timer at the top of the screenshot you showed. But without taking a deeper look, it's difficult to really know. Your best bet here could be to reach out to the store yourself and ask them directly, as Shopify would not be able to provide any detail or even confirm if it is a Shopify store for privacy and security reasons.
Hope this helps clear this up for you a little.
All the best, Nick
Hi Shopify Team, which plan do I need to be on in order to be able to add a payment logo to the checkout page? In AU the plans are Basic Shopify, Shopify and Advanced Shopify. Please don't tell me I need to be on the Advanced $299 per month being that I haven't even started selling or launched my store. I want the Partial.ly icon to appear in the checkout page making reference to the Payment Plan I have added: https://www.luxoftheworld.com.au/26441089068/checkouts/6ecdb317e1fe2a868ce033680f40886b?skip_shopify...
The checkout is something which can only be edited if you are on the Shopify Plus plan. When on the Shopify Plus plan you can edit the checkout via the checkout.liquid file.
You can see the guide Shopify has with more information about editing the checkout.liquid file here.
Sounds good @CFRG.
The cost of Shopify Plus does vary and certain aspects. Because of this, you can click in the top right corner of the link here where it says "Get Pricing" to find out more on what it would be to upgrade.