How to make these animated lines

Those are almost definitely particle effects and if they re-used the actual game assets, chances are that this is all rendered in the Unreal Engine directly as a cinematic, including the parametric particle effects from the game, complemented of course by traditional toon style renders and compositing. Re-creating something even coming close to this would require you to invest in a particle plug-in like Particular or for that matter even the whole Trapcode suite. AE doesn't have anything of that sort built-in. Admittedly, though, you could re-create soem of the simpler stroke effects using the usual methods like shape layer strokes, Write-On/ Stroke with masks, Roughen edges and lots of tweaking. It's just going to be a lot more work. Anyway, this isn't something you will find a specific all-encomapssing tutorial on, but you certainly will find tutorials on the individual sub-steps and techniques liek creating neon-like strokes, smoke puffs and so on. That and of course as I mentioned you may need to look into other programs as well, in particular some 3D stuff.

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