The short answer is yes. Twine itself has no effect on compiled games, so it would only effect your project if story format developers abandoned their projects, but since those are open source, other community members are free to step in and keep them working. That's the main benefit of open source.
Twine games are HTML documents, and while standards and browsers change, both actively try to support legacy stuff where possible for as long as is possible--new features are added, but it's rare for old features to be completely removed.
If that were to happen, it is the author's responsibility to update their game, usually by updating the story format and rebuilding it. But generally speaking, you won't need to outside of the rare quirk like Chrome changing how autoplay works for media, which may cause some games to have fairly minor sound issues if users use the default settings.
The odds of Twine games wholesale stopping working, and then the odds of no one stepping up to fix it, are extremely rare even in the long term.