Articulated arm wall-mount (13lb. LCD monitor), 25 gauge metal stud, 3/4" drywall
Point focused loads going into metal studs are not a good idea. You would be much better advised to install a piece of good quality 3/4" plywood to the wall that is big enough to span across two or three studs and have a height of about one stud spacing. Use multiple sheet metal stud screws to secure this plywood to the wall. Then you can install the bracket to this plywood with short large sized screws. If you drill proper sized pilot holes for the screws into the plywood they will have remarkable holding power. (You would not use those lag bolts that came with that bracket).

Note that the surface of the plywood will be a far better bearing surface for the bracket as well. If you installed the bracket directly against drywall there is a good chance that over time the stresses on the bracket back and forth will dig into the drywall and cause degradation of the wall surface and let the bracket get loose.

If good quality plywood is used it can be nicely sanded and painted to match the wall. It will be hardly noticeable behind the monitor.

If you have concern with the bracket screws just into 3/4" plywood you can always use the toggler bolts to hold the bracket to the plywood.