sorry, there was some confusion about your question. Requests to assets using the Delivery API or Preview API do count, but requests for the actual assets do not count as API calls, but they are counted in the bandwidth limit:
In practice, doing $asset = $client->getAsset($assetId) in the PHP SDK will count as 1 API call. However, actually displaying the image in your HTML (echo $asset->getFile('en-US')->getUrl()) will not count as an API call.