it's a month from the submission of a manuscript of mine in a "World Scientific" journal, but its status is still "Editor Invited". I just sent the editor-in-chief a note to ask about the situation because the editor assignment process is unusually getting long. The editor-in-chief did not answer my inquiry, so I am about to withdraw the paper. Let's say (s)he doesn't confirm my withdrawal request. Will I be ethically authorized to submit my manuscript somewhere else considering that I will keep the withdrawal email (in case someone claims that I hadn't withdrawn it before new submission)?
This is actually a really interesting question as I don't think there's a black and white answer to this. Ethically, a "reasonable" attempt must be made to confirm withdrawal of the manuscript. People will draw the line at different points.
I would argue that one attempt at contact is not sufficient to be considered reasonable. If possible, I would contact the editor by phone as well as email. Check to see if there's a withdrawal protocol through your online account or if there are any additional contact details of committee members.
I would only feel comfortable submitting elsewhere if I had made multiple attempts to contact the journal over a period of 4-6 weeks. But that is just my opinion. I'm interested to see what others think...
Will I be ethically authorized to submit my manuscript somewhere else considering that I will keep the withdrawal email (in case someone claims that I hadn't withdrawn it before new submission)?
No, I think you need to receive the official withdrawal confirmation from the journal, as long as the journal that you have submitted your manuscript is not a predatory journal. I assume it is not predatory cause World Scientific is not that kind of publishers I believe, at least in my own experience with them.
You mentioned that you have contacted the Editor-in-Chief of the journal and he/she did not respond to your inquiry. I think EiC is not the right person to contact in case of withdrawal. I don't have experience with withdrawing a paper in World Scientific, but in my experience with Elsevier, usually this process is handled by associate editor or even administrative section of the journal. If those people also did not respond to your inquiry, I think you need to find a more direct contact way like phone to get in touch with them and see what's the procedure to withdraw the article. If all of these suggestions failed in a timeline of 2 or 3 weeks, I think you need to assume that maybe the journal is indeed a predatory journal.
For the last moment that you want to submit your manuscript somewhere else, please read the current journal's policy and agreement that you agreed upon your submission to find out if you give them your consent to publish your work or not (which I think you did cause otherwise submission to be considered for publication is meaningless...). Cause, if you failed to receive a response from them and if they are indeed a predatory journal, it has a really high chance that at some point in the future, they will publish your work and if you already submitted somewhere else or get accepted in another journal, you may ran into some copyright and dual publication issues with both journals.