I fixed and it is no longer connected to parkway. As of small park being inside bigger park, it is a newly opened park, which is actually a small installation and a sign that says "იოსებ ჟორდანიას სკვერი". I am not sure if its just that small bit or if they named whole park around that name. But the signpost is only standing in the newly opened section and not standing at any entrance of the bigger park, which makes me wonder.