There are many ad-on spell checkers and they are free. The default for this forum is IE-Spell and I have to say that when I used IE it was more than adequate.
If you are using Chrome it should have its own built in spell checker. If that is the case then it's Google's issue not ours.
The difference between your Android Phone and the website is that your Android is an operating system and the spell check is an application. This is a website and does not run applications. You have to add the application or ad-on to your system.
I don't know of any website that has a built in "spell checker".