Line of sight and shadow casting aka field of view are two different things. LoS determines whether two points (eg the player and a guard) can see each other. FoV determines which points/tiles are visible from a single point. LoS and FoV may also take into account the direction you're facing. If you want a tile-based FoV you could use a LoS algorithm to calculate a FoV by just running it repeatedly for every tile on the screen, but that's really inefficient, and the OHR's script interpreter is far too slow for it to be feasible. Still, the two are very closely related, and if you create a game that uses separate LoS and FoV algorithms you want to try and ensure that they agree on visibility.
Also, there are FoV algorithms (prehaps they should be called something else; I'll call it "light casting") which try to determine lit squares rather than visible squares. Then you place a light source at the player, maybe more throughout the level, and possibly allow light to bounce around corners. In fact you may just ignore walls and get something very simple.
Breshenham's Line algorithm is for drawing lines, and is one of those things that's so obvious once you understand it that you wonder why it's named after someone. I would avoid the Wikipedia article, instead look at this figure from it:
Naturally, drawing a straight line is pretty easy, just involving some simple math. Anyway Breshenham's algorithm is used for LoS by tracing a line from one point to the other and checking whether each tile on the line contains an obstruction. Notice that it allows sight past two obstructions that are diagonally adjacent. This is fine if your obstacles are barrels and you're meant to be able to see diagonally past them, but not if they're cubes of concrete. Also, it isn't relevant for non-tile based LoS at all, such as in that video you posted.
Although you are looking for FoV and not LoS, an full-featured implementation of Bresenham's is available at
http://rpg.hamsterrepublic.com/ohrrpgce ... e_of_sight which also links to a less scary simplified version.
Drawing pixel-based shadow casting is possible in theory in the OHR using slices, but again the script interpreter is far far too slow for it to be practical. However you could draw larger chunks, like quarter tile 10x10 black squares. That could be fast enough, and you can use a tile layer for it rather than slices.
Also, you could instead use Cyberdogs/C-Dogs-style shadow casting, which draws shadows only at 45 degree angles, and is very fast to calculate. In the following screenshot you can see the shadows are blocky because they're tile based, but it would be easy to draw sharp diagonal shadow edges instead. I've always wanted to make an OHR game which does this, or even a full Cyberdogs clone (they're both great games).
There are a couple OHR games that do some kind of (tile-based) "light casting". The earliest that I know of is
Project `C'. In that case you can see through walls.
Ortega Colonies did something where light originates from the player and other sources and can flow around corners. Scripts for that are available.
The Dungeons of Koh-Lah'B is another example. I know there was at least one more. However I don't think I've ever seen an OHR game with real FoV; Ortega Colonies is the only one I know of that even takes walls into account.
(On the other hand there are quite a few OHR games that do LoS.)
The Roguebasin article on
FoV has a bunch of different algorithms of course, but translating other languages to Hamsterspeak can be surprisingly difficult.
