The ZEOS component consists of several packages, and when you install zcomponents.lpk first the IDE does not know where the others are.
In "Packages" > "Open Package file", open first zcore.lpk, then zplain.lpk, then zparsesql.lpk, then zdbc.lpk - just "open", no need to "compile" nor "install". Finally open zcomponent.lpk and select "use" > "install". Now it should work.
The easier way is to use the Online-Package-Manager (in menu "Package"): scroll down the list, check ZeosDBO, click Install and answer the few questions. Wait until the IDE is rebuilt.
You will get version 7.2.14 of ZEOS this way. If you need the latest development version (some v8.x) you must do the steps as described above.