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I don't understand what you did. For one thing, you have to download a format, and open it using the Format button. Don't just put it in the metadata by hand, it doesn't work that way. And it sounds like you never published the game either. The editor would have warned that you don't have a format loaded.

Chapbook's site says:
"Chapbook is a story format for Twine 2, which means that it plays stories created in Twine in a web browser. To use it, add this URL as a story format:"

So in Tee-Wee I put that web address in for the format, on the line where you put the file name.

Then I clicked publish, and it did allow me to do that. It didn't warn me that I didn't have a format loaded.

But then when I clicked to open the file in my browser when it asked if I wanted to, it opened it in Edge or Internet Explorer (not sure which) for some reason.

It had a lot of lines like the one I pasted in my first comment, but otherwise was plaintext a bit of what I'd entered in.

Today I'm refollowing those steps so I can express it clearly, and instead of mostly readable with strange lines, in Edge it's got this a lot:

 * Copyright (c) 2014-2016, Jon Schlinkert.
 * Licensed under the MIT License.
 */var r=n(39),o=n(41),i=n(42);e.exports=function(e,t,n){return r(e)?o(i(e,t),n):o(e,t)}},function(e,t,n){"use strict";
 * isobject <https:"" jonschlinkert="" isobject=""></https:>
 * Copyright (c) 2014-2015, Jon Schlinkert.
 * Licensed under the MIT License.
 */var r=n(40);e.exports=function(e){return null!=e&&"object"==typeof e&&!1===r(e)}},function(e,t){var n={}.toString;e.exports=Array.isArray||function(e){return"[object Array]"}},function(e,t,n){"use strict";

In Chrome, though, it looks more like this:

.small-caps{text-transform:uppercase;font-size:70%;letter-spacing:.075em}#backdrop{min-height:100vh;align-items:center}#backdrop,#page{display:flex;justify-content:center}#page{flex-direction:column;width:40em;min-height:calc(100vh - 2em);max-width:calc(100vw - 2em);line-height:150%;margin:1em;padding:4em 4em 2em;position:relative}#page article{flex-grow:1;display:flex}#page article>:first-child{margin-top:0;width:100%}#page footer,#page header{display:flex}#page footer>div,#page header>div{flex-grow:1}#page footer p,#page header p{margin:.5em 0 0}#page footer .center,#page header .center{text-align:center}#page footer .right p,#page header .right p{text-align:right}#page header{margin-top:0}#page header.has-content{border-bottom:1px solid #000}#page header.has-content+article>article>div>p:first-child,#page header.has-content+article>div>p:first-child{margin-top:1em}#page footer{margin-bottom:0}#page footer.has-content{border-top:1px solid #000}#page hr{border:none}#page hr:after{content:"* \A0   * \A0   *";display:block;text-align:center}#page .error,#page .warning{font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Oxygen-Sans,Ubuntu Cantarell,Helvetica Neue,sans-serif;font-size:80%;background:#fff5f5;color:#c92a2a;padding:.5em;border-left:4px solid #ffa8a8;position:relative;margin-bottom:1em;overflow:auto}#page .error :first-child,#page .warning :first-child{margin-top:0}#page .error :last-child,#page .warning :last-child{margin-bottom:0}#page .error a,#page .warning a{color:#c92a2a}#page .warning{background:#fff9db;color:#e67700}#page .warning a{color:#e67700}#page .fork p{display:flex;flex-direction:column;width:100%}#page .fork p a{display:block;flex-grow:1;text-align:center;padding:.5em}@media screen and (max-width:768px){#page{margin:0;width:100vw;max-width:100vw;min-height:100vh;padding:1em}}#spinner{position:absolute;bottom:0;right:0;opacity:0;transition:opacity .25s ease-in-out;pointer-events:none}#spinner.visible{display:block;opacity:1}
*{box-sizing:border-box}body{margin:0;padding:0}img{max-width:100%;height:auto}input[type=text],select{padding:.25em}pre{white-space:pre-wrap}tw-storydata{display:none}</style></head><body><form id="cb-validation" action="javascript:void(0)"><button id="cb-validation-tester" hidden></button> <button id="cb-block-enter-key" hidden></button><div id="backdrop"><div id="page" aria-live="polite"><header><div class="left"></div><div class="center"></div><div class="right"></div></header><article></article><ul class="warnings"></ul><footer><div class="left"></div><div class="center"></div><div class="right"></div></footer><div id="spinner"><img 
(1 edit)

Yes, the instructions on the Chapbook website are for adding it to Twine 2. Tee-Wee is a different application, that works differently. You need to first download the format, then load it using the Format button, then Publish. In fact the latter should stop after warning you there's no format loaded; if it doesn't, that's a bug. I'll look into it.

Edit: looks like I misread. Frankly, I've no idea what's going on there. Looks like Tee-Wee did load the format straight from the site (somehow), but when you published the game it actually just saved the raw data?! Just try downloading the story format and loading it from disc like it's supposed to work.

But it doesn't offer a download. There isn't one at that site at all. The only way to use it is to add the URL.

Unh... you can download the Javascript file, either with a right click on the link, or with Save As after it opens in the browser. It's still a file like any other. Either way, you can't expect to put an URL in a file opening dialog and have it work correctly.