Hello,
I have been able to run the Natural Language API demo in [1] with Chrome Version 87.0.4280.152 (Official Build) (64-bit) but I cannot yet update my Browser to a newer version so I have not been able to check if this behaviour occurs in every computer with chrome browser version >=88.0.4324.104 or if it has to do with the cache of your browser.
It seems like the issue you are experiencing is indeed related with the captcha system in [1]. Is this the only page in which you cannot see the captcha? Have you tried to clear you cache or to access from an Incognito window in case there was a previous failure when filling the captcha and your browser is being recognised as a robot?
You might want to report an Issue with the new version of Google Chrome following the steps on [2], given that the API in [1] is working properly and the issue seems to be on the Browser side that does not display the captcha.
[1]:
[2]: