All their media is hosted under the redditstatic domain, and as far as I can tell, that's hosted on AWS. (There's actually also a redditmedia domain, which they may also use, but that's also on AWS).

That probably means that Reddit can get away with saying they don't host any of it. They merely point their web addresses at the third party host.

~~Not since the last half decade.~~

edit: i read the comment backwards. oops.

From article

Reddit challenged its designation on the basis that it is mostly a text-based discussion platform, and links to videos uploaded elsewhere on the internet should not be factored in. The Irish regulator counter-argued that the audio-visual content on the platform is extensive, and pointed to its enormous reach, with 73 million daily users.

Could not find any post statistics, but they probably are correct and percentage wise uploaded videos should be at the bottom, but total count probably is too large to be simply disregarded. Reddit probably has more videos than Vimeo which is purely video based. And if Reddit would be in the clear then so should be Twitter and Facebook since those too are primarily text based.