There's too much to say really. You have your script and style tags outside of the html block, you should at least put the script tag in the head element. You have a superfluous "1" in the code that can cause a compilation error and stop any js running.
current = "x"1;
Your ChooseSquare function checks
if (document.getElementById("button1").onclick)
onclick is an event handler, you are simply asking if button1 has a click event handler, which it doesn't so this will always evaluate to false. Even if it evaluated to true, the code inside sets the value of "button1" to "x" however "button1" is the row, not the button, and a row can't have a value.
After a huge list of button checks that set to x you then do the same to set to o, but the code makes no attempt to set the value to "current". There is too much duplication in your code that could be handled with functions instead.
You need to throw this code out and start again from a better, simpler design. Give each button a click event (they can all use the same function for the click event), on that click event set the value of "this" to "current" and then change the value of current to be "o" if it is "x" and "x" if it is "o"
JavaScript 'this' and Event Handlers — SitePoint[
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