I see your point but it requires the prior knowledge that the link will log you in into the app.
I have not possessed that, and the mail did not hint that, only told me to click, and I expected to get some means to enter a new password for the email, or to acknowledge my identity, or else. Or, at least, that it would actually turn out what the link does.
My suggestion is that the website should realise that the link has been clicked on a computer (or, really, on any device different from the phone in question) and tell the user what to do, and what not to do. Offering a meaningless error is probably the worst possible way to handle this user error.
(As a sidenote it would have been impossible for me to read the email on that specific phone, but copying the link and then entering into a browser made it possible to click it on. I’m possibly not the average use case. )