Despite the scary warning, installing under 1.35a works fine, and at a glance I don't see any reason in the code why it wouldn't. Anyone knows what that's about?
Topic on Extension talk:HitCounters
The warning is about doing upgrades, and loosing the "old" visitor counts from the "page" table because upgrade.php of MediaWiki 1.26 and newer deletes them. Have a look at Extension talk:HitCounters/Archive for details. (You can also run the migration SQL from https://gerrit.wikimedia.org/r/plugins/gitiles/mediawiki/extensions/HitCounters/+/master/sql/ manually before updating to 1.26 or newer.)
If you do a new installation and don't have any data to migrate, you can IMHO ignore the warning.
That's the opposite of what the template says, though (Currently it is only possible to migrate wikis using MW 1.25 to use this extension. A fresh install in MW 1.26 and higher is not possible!).
Please re-read the template - the important part is the word "migrate", and all text in that box talks about migration and updating. The next sentence after what you quoted says (highlighting done by me)
[...] an update to MediaWiki 1.26 or newer can permanently delete your hitcounter numbers! See task T120216.
So if you ignore this warning, you will loose the old visitor count from the page table - but in a fresh installation, you have 0 visits, and therefore don't loose anything.
That's at least how I interpret this warning, and also what I expect based on the experience with this extension. Besides this, the fact that it works for you in a fresh install also confirms this.
So: don't worry too much ;-)
Updated the warning.