I'm not an expert in this area but, according to Adobe, it depends on the use. For rasterized images, PDF documents, etc., the answer seem to be 'yes':
> Does my client need their own font license to use the designs? No, not if you are creating graphics or documents that have rasterized or properly embedded font data, such as a PDF, JPEG, or PNG.
> However, if your client needs to have the font installed to edit your design, they will need their own license, either through a Creative Cloud subscription or as a desktop license purchase.
But for websites, the answer seems considerably more complicated but, essentially, 'no.'
> Can I use web fonts for my client websites? The Terms of Use do not permit reselling beyond December 31, 2019. After that time, the client's website must load Adobe Fonts from their own Creative Cloud subscription to ensure that there isn't any interruption to the font licensing or web font hosting.
> Please refer to the full Terms of Use for more information on what reselling the service means, and related definitions. . . . [A few more paragraphs about how to switch things over from your CC account to a client's.]
https://helpx.adobe.com/fonts/using/font-licensing.html
Reading between the lines there just a little bit, it seems like Adobe may have run into its own licensing issues. And this all depends on Adobe being correct that they have gotten a license from the creator of the font that allows Adobe, in turn, to convey these rights to the CC subscriber. Uncertainty on exactly these points--Does Adobe allow clients to use the fonts without their own subscription? Does Adobe itself have the rights to allow this?--seems like the root of the issue in the article:
>The one useful Adobe representative we spoke to on the phone last week mentioned that numerous people are having trouble with the Adobe licencing with this particular font. She said that Adobe may not have the appropriate licencing for this font listed on the website – unsure if this is reliable information or not, but thought I’d mention, as if this is the case, there should be more information clearly visible on the font’s webpage about how to use it correctly.
>From our understanding, we have used the font in the correct way (according to the Adobe Web Project method). However, our client does not have an Adobe subscription, so we concerned that we are not covered by the Adobe licence due to this: https://helpx.adobe.com/fonts/using/font-licensing.html.