google-groupsusenet
Is it possible to see the tree structure in the usenet archive (since Google currently appears to have broken it – removed it completely)
I can't find any images to show how Google groups did used to show a tree structure for usenet groups. But they did.
I am more interested in free ways to do so.
You can post a message to a closed thread thus:
Source: http://groups.google.com/group/google-web-toolkit/msg/c3e3e6f250f4dcd6
I figured it out.
Go to https://groups.google.com/
If you use the old interface for Google Groups click the button "Switch to the new groups". 
It should sit in the lower right corner of the browser window. If you cannot find it, visit https://groups.google.com/d/?fromgroups Now set the new interface as default.
Try going to https://groups.google.com/ You should now see only the new interface. It will redirect you to https://groups.google.com/forum/?fromgroups#!overview
From here, click on the "Browse all" link. It will take you to https://groups.google.com/forum/?fromgroups#!browse Here you should see the group categories as you're used to with the classic Google Groups interface. Only here you will not see any icons for the categories, just simple blue links. I guess it fits better with the new interface design.
Now here's what happens if I click on the "My groups" link from here.
Click on "My groups" link on the left. It will take me to https://groups.google.com/forum/?fromgroups#!myforums It says "You also belong to groups in 1 other organization. show; View 1 group at googleproductforums.com" 
Click on the link. It takes me to https://productforums.google.com/forum/#!myforums "Google Product Forums (59 subgroups)" 
Click on the "Home" link on the left. It takes me to https://productforums.google.com/forum/#!overview
Click on "Browse all" button. It takes me to https://productforums.google.com/forum/#!forumsearch/ and it shows all the subgroups... I think. 
So my conclusion is that https://productforums.google.com and https://groups.google.com/ are not the same thing. Go figure! The former uses Google Groups service, but it is a separate Google website. It has no browsing of groups (subgroups actually) by category, since there are no more than 59 subgroups to Google Product Forums or 277 subgroups in total.
The same is true even if you use the classic Google Groups interface. So just make sure you are actually at https://groups.google.com/ and not some random website URL that only uses the Google Groups service and is not actually "the" Google Groups [website].
Best Answer
Tree structure of Google Groups/Newsgroups (not OP's question)
Google Groups has done away with their tree structure navigation format for browsing Google Groups in favor of breadcrumb navigation. This makes sense as a tree structure isn't very useful given how Google Groups is both a web gateway to NNTP as well as a web mailing list not compatible with Usenet. Since anyone can create a public or private Google Group, a tree navigation quickly becomes unwieldy and it doesn't appear Google cares to segregate the services; instead choosing to rely on its search tech.
A Usenet hierarchy is, reduced to its essence, a set of Usenet newsgroups that share a common naming prefix, with "." used as the separator between the levels of the hierarchy, like host names. The most popular list is provided by the Big-8 Management Board (B8MB). They publish a list of the canonical Big-8 Usenet groups to news.announce.newgroups every month and can be viewed via Google Groups at http://groups.google.com/group/news.announce.newgroups?hl=en (also mirrored at ISC, ftp://ftp.isc.org/pub/usenet/news.announce.newgroups/Group_Lists/)... It does seem silly Google Groups doesn't integrate a hierarchical list option for just NNTP groups...
While Google Groups is the most extensive collection, there are other free public News servers you may want to explore, including getting a free NNTP account so you may use your own newsreader. The free NNTP accounts will not have as an extensive history however, so you may want to try to make Google Groups work better for you.
Join/Star groups of interest: Most people who use newsreaders subscribe to newsgroups which is akin to "Joining" or "Starring" a group via Google Group's interface so you may want to browse that list for groups you find of interest.
Use keyboard shortcuts: For instance if you know the type of group you are looking for, you can use the hotkeys
glto quickly go to a group or search for similar newsgroups.glcomp.unix[Tab][Tab][Enter]Keyboard shortcuts may be shown by typing the question mark character on any page within https://groups.google.com or at https://support.google.com/groups/answer/6148722
[Updated: answering refined question]
Tree structure of messages in Google Topics (OP's question)
To reorder messages into conversation threading (messages will be reordered to who replied to whom and then chronologically):
1. Navigate to any Google Groups Topic
2. Above the first message/post, click on the Topic options icon:
3. Click option "Tree view"