Shared queries are set up under the Team Area under each project in RTC Eclipse client. To see them in the Web UI, one needs to add the user to that team area, so that the shared folder and queries are visible.
The web client checks that you are a Team member very strongly, as opposed to the Eclipse client. If a user is not listed as a team member, even though he is the query author and the one who shared a query, it will not show on the web.
As a work-around, in personal dashboard one can add a query widget which shows all queries from different teams. In general, the RTC Development team believed that web views should only list the 'Shared in Team' queries where the user is a member of the team.
This is tracked in this work item, which was logged as a defect in jazz.net:
So for end users, as curious as I about this behavior, I hope this note helps.
P.S: At the time of writing, I have tested this behavior in and upto RTC 4.0.3 version only.