Regardless of which you choose, you need to be more clear with your button labelling. The buttons should either read:
Previous Result || Back to Search Results for XXX || Next Result
or it should read:
Previous Article || Next Article
You got here by searching for XXX. Return to search results.
Depending on the functionality you actually intend.
Either solution is valid, but creates additional requirements for the design. Firstly, a solid design heuristic is to avoid forcing users to recall information they entered earlier. Instead it's much better to remind them of their choice - hence why it's important to reiterate their search query if you're expecting them to want to navigate through the list of search results.
The other thing that's worth noting is that if you're navigating by search result you have to be consistent with the ordering on the search page - if there are multiple methods of ordering (relevance/recency/whatever) this has to be preserved in the horizontal navigation through the results.
The major drawback with the SERP-focused method is that it is complex and requires the user to be aware of context (even if you can remind them of the context). It may be more useful to your users to have horizontal navigation relate to the category of product they find themselves in (or perhaps other products in the same conceptual "space"). In addition, this may be functionality that your product owner wants but none of your users will find useful (or might even find confusing).
You need to perform user testing to discover whether this feature is necessary, and which solution to choose. Make sure you match your users' needs and mental models, not just what the product owner (or even you) thinks might be the best solution.