The rules for being listed onto the Shopify App Store, including the specific sales channel requirements (section 13) are available in our help center here.
To answer your other questions I would need a bit more info, how would you be using the checkout API? Just to create web checkouts and redirect the customer there? Or would you be performing payment processing yourself?
Also chapter 13. is very unspecific:
A sales channel app lets merchants publish their products from their Shopify admin to your platform, whether they're selling online, on mobile apps, or through social media.
I'm currently not offering a Platform or Marketplace. Each Merchant, that installs my app gets its own additional storefrontend with its own (Sub)Domain and a custommizable view.
My only argument is, that for the merchant, it can be seen as an additional sales channel, but not in the way Platform or Marketplace like Amazon, Ebay, Facebook, Pinterest can be, where all merchants are presenting on the same Platform.
So still my question is, how strict are the requirements from shopify side, in case of Platform or Marketplace concept, to allow the usage of the checkout api? In terms of the Admin Interface (with the use of polaris e.g.) I can fulfill all these requirements.
Sounds a little bit like a mobile app builder if you are building a custom storefront, but not necessarily mobile only.
To my knowledge the only restriction is that you cannot bypass the Shopify checkout, it must be used to process payments.
You can DM me additional details and I can look into it, but the requirements are all listed on the previous page I linked for all different types of app categories.