As the runtimes license is currently written, redistributing the Spine Runtimes is allowed without a Spine license as long as the users of your product obtain their own Spine Editor license.
I suppose the product in your case is the web page and it's probably not feasible to ask all your web visitors to first get a Spine Editor license. Given that, then you would indeed need your own Spine Editor license. Spine Essential is sufficient unless you earned more than $500k gross in the past 12 months, then you'd need Spine Enterprise. You can provision Spine Enterprise for zero users if you only need it for the Spine Runtimes.
This doesn't come up as often as it might seem at first because almost everyone using the Spine Runtimes already has a Spine Editor license to create or edit their skeleton data. We would like to revise the Spine Runtimes license to make it usable on websites and to clarify the terms for those without a Spine Editor license, but I can't say when we'll find time to make that happen.
