You don’t really get anything like a modern concept of light, as something that comes from the Sun (or whatever), bounces off objects and then into your eyes, until the work of the Muslim philosopher Ibn al-Haytham (a.k.a. Alhacen or, more commonly, but incorrectly, Alhazen) in the 10th or 11th century. Before that, light was not really considered as something that traveled at all. For Aristotle, for example, light was the power that the Sun, or a flame, had to make the air transparent.
It may well be true that no-one had much idea about the actual speed at which light travels before Rømer. However, once you have the idea of it as something that travels at all, you can certainly infer that it travels faster than sound by noticing that you can sometimes see a distant event, such as a lightening flash, or an avalanche on a distant mountainside, well before the sound that it makes reaches your ears.
But as Pliny lived well before the notion of traveling light, I am not sure what he might have been on about. Is it possible we are dealing with a mistranslation or an editorial “improvement” by some medieval scribe? (I cannot locate the passage you mention. Perseus seems to be telling me that book 2 of the Natural History only has 113 chapters.) Once your head is infected with a modern conception of light, it can become hard to imagine that people have not always thought of it this way, and it seems quite possible that some scribe or translator has somehow fixed the text to make it say what they think Pliny must obviously have meant to say.
In Pliny’s time, the most widespread ideas about how vision works involved either atoms from the object’s surface entering the eyes (these travel, but they are not light), or else, more commonly, some sort of influence (that was, perhaps, fiery, but not light as we think of it, despite the fact that some modern sources insist on calling it light) reaching out from the eyes towards the object to be seen. In the hands of mathematical theorists like Euclid, Ptolemy, and the Muslim Al-Kindi, this is analyzed in terms of rectilinear rays that reach out from the eyes towards visible objects (this allowed them to give quite accurate mathematical accounts of various aspects of perspective), but, to the best of my knowledge, they did not really think of these in a dynamic way, as traveling out from the eyes. Plato does talk about fire coming out from the eyes when we see, however, and Galen (and the Stoics) talk about visual pneuma emanating from the eyes, so I suppose it is possible that Pliny thought of these visual rays as traveling outwards. (I sort of doubt it, though.)