To watch YouTube through a browser on KitKat, download a compatible third-party browser:

To help find the absolute best setup for your vintage device, could you share a few more details? Please let me know: The exact of your device.

Install the APK and start streaming instantly without signing into a Google account. Method 3: Browser-Based Streaming via Kiwi or Opera Mini

To install this version, you must manually download the Android Package (APK) file from a trusted archiving site. Step 1: Enable Unknown Sources