"Extraordinary claims require extraordinary evidence", and this is the weirdest star we've seen. Your claims of clickbait are out of line, because we really don't know and alien megastructures is a reasonable theory.
That can't physically work: for one because the parallaxes would be different and almost never line up. If something's colinear with a star today, it won't be colinear 6 months later, when the Earth's on the other side of the sun.
At 2 light years for instance, that spacecraft would trace an apparent ellipse 3.3" in diameter, while Tabby's star (1,480 ly) would be stationary (0.004" parallax). In comparison, the star's apparent disk is just 30 μas wide (0.00003").
This is an amazing theory. What could possibly be more out there than alien life? Alien life in a gigantic spaceship accidentally coming between you and a star.
Going from e.g. Earth to Mars does not consist of aiming for Mars and firing your rockets. It consists of hitting a parabolic transfer orbit and then doing another burn to place yourself in Mars' orbit -- or just heading right in if you've got the heat shields and retropropulsion for that. Basically you do orbital mechanics like Wayne Gretzky: you don't go to where the planet is, but where it's going to be.
Would interstellar flight be that different? Wouldn't you be executing a "transfer orbit" about the galactic center? Or is the effect of galactic-scale gravitational pull negligible there and you just end up basically going straight from A to B?
Edit: turns out this came from an actual subreddit dedicated to this star!
The galactic center is 100,000 lightyears away. Going from a location to another 1000 lightyears away via the galactic center would make the trip 200 times longer. A 10,000 year journey would thus take 2 million years. It's probably better to jump from point A to B, then.
I would think that by the time they actually move some meaningful distance, their sun would not be 'behind' them anymore, they'd still be moving toward ours, but as the whole thing is constantly moving, their sun would have moved relative to ours.
And 'alien megastructures' isn't even the most ridiculous idea: https://www.reddit.com/r/KIC8462852/comments/4w7qfi/ben_mont...