I am not as certain as you (and the authors / scientists in this article) apparently are. First, natural fires from lightning are not that uncommon in the primeval forrest. Even in wet forrest conditions, smoldering coals would be easy to find by smell alone. Learning to find, feed and preserve live coals would be an optimal survival characteristic easily in the capacity of H. antecessor.
Making fire, on the other hand is a rather complex task that I failed at many times as a Boy Scout. The most likely method available at the time would be the hand drill method, using a somewhat thin, flattened wood platform with a formed pock to hold and steady the drill. Underneath the wood platform you gather easily ignited tinder to catch fire. You take and spin the drill between your palms (it quickly hurts) in hopes that the wood of the platform (choose carefully) is dry enough and softer than the drill wood so that as you spin the drill, friction causes the bottom of the hole to reach the smoke point before you penetrate the bottom. The idea is that when you do penetrate, the semi-ignited coal at the breakthrough point will fall into the tinder to ignite it for a flame and fire.
A better method is the bow drill but I think that unlikely at this point of tool-making. It appears the H. antecessor had minimal tool making and if they had a bow, where were the arrows (joke!) I give enormous credit to our Neolithic and pre-Neolithic ancestors. They survived the natural world (red of claw and fang) as well as the Ice Ages. I just look at the circumstances and believe that retaining a live coal from a prior fire was a major survival trick for GENERATIONS. That bright boy who found out to drill for fire probably took a long time before he came along!
Teleology.
The bow was a huge advance from the hand drill for sure. I also imagine they kept a fire going constantly once a fire source was found. When the winters started getting hard in Europe, anyone who stayed would just about have to have figured out fire making. It’s hard to find preserved copies of ancient tools as lots were doubtless made of wood or weaved grasses, etc.