That blog post is mostly just about the apps. Sadly we still have a lot Google services in use afterwards, like e.g. the optional location service which speeds up the GPS positioning, but those parts are much harder to replace :-/
Some time ago MicroG[1] was set to solve that problem, but I don't know how far they have come.
"LineageOS 14.1 without the Google apps" (from the OP)
Google apps/Gapps is what MicroG replaces. Gapps is an optional, separate install not included in LineageOS. Location services etc are part of that.
MicroG works well, I use it on one Android device and have another using LineageOS without either Google apps or MicroG. Both devices are extremely useful and capable and do everything I require, but I've never let myself become dependent on any Google services in the first place (despite having been a web dev for almost 20 years).
Some time ago MicroG[1] was set to solve that problem, but I don't know how far they have come.
[1]: https://microg.org