Hello,
There is a slight difference between an asset loading and an asset making requests . The plugin loads the asset once, and you can verify this by viewing your website source directly. The Network Tab shows requests being made by your website and any of the loaded scripts. The ReCaptcha API (api.js), once loaded, goes out and makes further requests. Presumably, verifying that your ReCaptcha key belongs to you and your domain. We have no control over any requests the API makes since it is provided by Google.
Additionally, you can see that these requests are quite small and take fractions of a second. The right-hand side of your Network Tab image is measuring these requests in milliseconds. We know there are 1000 milliseconds in a second. If we add up all the requests, including the loading of api.js (not highlighted in your screenshot) it comes out to 179 milliseconds. That is less than half a second ( 0.18 seconds ) for the API to load and then make the additional requests that it needs to function properly.
Hopefully, that answers your questions and concerns, but if you have anything else, please reply back to this thread and we can assist further.