Hello! Welcome to OSM. So even though its not a through road, it does seem to exist on the ground as a dead end road. It should only be removed if its been completely demolished and does not exist at all on the ground anymore. But it leads to two driveways so that seems unlikely.

Normally just putting a gate along the road with "access=no" and "locked=yes" is enough to stop routing software that use OSM data from Routing people along that way. So right now because the way is not connected, and there is a locked gate feature, no routing software using OSM data should route anyone through there. (once the changes propagate, and that could be a while)

If the gate could theoretically be opened and let cars through it really should be one connected way, just with a gate node. But Its hard to tell if the road really did stop before the gate, that's why I stopped the road short a little before the gate. If you are from this area you can be a better judge.

If that dead end road is officially not open to the public you can use the tagging system to tag "access=no", or "access=private". But don't abuse these tags, if its a public way and the public is allowed right of way through there, don't use these tags.

Just a general rule, if it exists on the ground, it should not be removed from OSM regardless feature being public, private, designated or even informal/illegal/unauthorized. 

Let me know if you have more questions! 