Just to clarify - browser games are completely safe and absolutely cannot do something like run an executable on your computer. Browsers are essentially a strong kind of security "sandbox" and have permission prompts to access anything potentially sensitive like your camera or microphone, and if you don't trust the website you can just deny permission and that's that.
If you run an executable, that is something much more risky, as it could be some kind of malware, and downloaded desktop apps have far broader permissions by default - such as being able to read and write files, run other programs, access your camera and microphone without asking for permission, and so on.
A possible source of confusion is Construct can export your project as a desktop app, using options like NW.js. This then does potentially have all the risks of desktop apps noted above, since those are all risks with any desktop software. However if you are only loading a HTML5 game in a browser, then it's basically completely safe and cannot harm your computer in any way.