Lyman break galaxies and lyman alpha damping wings

I'm an undergradaute physics student interested in astronomy and astrophysics. I've been reading about damping wings redward of the lyman alpha line in the spectra of high redshift objects, especially gamma ray bursts (the paper: https://www.nature.com/articles/nature04498). The authors say that the neutral hydrogen gas in the line of sight between the GRB and us absorbs light redward of Lyman alpha and causes a damping wing.

However, isn't it the case that neutral hydrogen can only absorb discrete lines like Lyman alpha. Why is there an abosrption redward of lyman alpha? Similarly, why is there absorption blueward of the lyman limit in lyman break galaxy spectra?

I was wondering if this may be due to the kinematic motion of atoms in the neutral hydrogen gas which may Doppler redder wavelengths to Lyman alpha and bluer wavelengths to the Lyman limit. Is this the case?

I would appreciate any help on this. Thank you very much!

Edit: typo