Well, I don't do a whole lot of building the DOM this way, using jQuery or anything else, but I do spot some simple errors in your code.
for (var z = 0; z < theBuyIns;; z++) {
Those two semicolons together will cause an error, because it expects after the first of the two it will find an expression (z++). So take out one of the two semicolons.
tr.append("<td>" + TDStatus.Vars.Players[z].Rank; + "</td>");
Actually each of these lines has an extraneous semicolon (after TDStatus.Vars.Players[z].Rank in this case). Remove them.
$('table').append(tr);
This is probably OK. I tend to reference things by ID, so I immediately thought this needed a # in front of "table", but this will reference every table on the page and append the rows to it. If this is what you want, then OK.