UPDATE, for anyone who strikes the same problem. Turned out to be a small issue, with a simple solution.
Because I was on a slowish connection I had uploaded Tiki 14.0beta.zip via FTP to the cPanel file manager on our shared hosting site. Much quicker than extracting on my machine and FTPing all the files.
Then I extracted the .zip to the sub-directory I'd made for Tiki. However, when I pointed my browser there to begin the Tiki install I saw only the sub-directory's index, listing tiki.14.0beta. Clicking on that I was able to install Tiki.
But after installation, pointing to the sub-directory still only showed the sub-directory's index. That didn't seem right so I ran to the Docs, read the bit about the ReWriteRule and posted my question here.
What I didn't realise until I took a closer look at the zip-file was that the Tiki files inside the zip were themselves inside a folder.
Then it was clear why my browser couldn't go straight to Tiki. I uninstalled as per Rick's instructions above and started again, this time simply renaming the extracted Tiki 14beta folder to our chosen sub-directory name. And all was well.
I haven't made the ReWriteRule change. Been hard at work getting to know Tiki and adding content. Having a great time - I love Tiki already. After months of researching all the Wiki and CMS options out there, I'm so glad we chose this one.
If I find later on that I need to make the rule change and get stuck I'll post a new thread.