There are a half a dozen outstanding exercises I can think of for delt thickness/mass but theregular lateral and front raise are not one of them. The lateral raise may have a place in some special delt routines (see below..... as well as pre-exhaust, detail/refinement work, etc) but hardly ever would anyone need front raises. Serious compound movements trumps them both for pure muscle mass gained.
Also that video clip offered for the push-press looks more like a jerk-press. With the push press, the bar is resting on the heels of the hand (bar inline with the wrist/forearm for better leverage & power as opposed to the regular thumb hooked over the bar grip) and usually taken off a power rack. There is a slight knee/hip thrust at the start of the push, pushing (not pressing) the bar overhead. That bar resting on the heel of the hand is also used by a lot of heavy benchers.
If you want to come to the point of being forced to buy new shirts and jackets because your whole shoulder girdle increases in muscle size, than consider a few of these.
1) Front press, preferred off a rack. But just press the bar about 3/4's of the way up. This keeps the delts (and tension on them) doing the blunt of the work. This also builds the lateral delt head and to a lesser degree, the rear. Apply the push or jerk version here if you wish. Control the bar at all times.
2) Press behind the neck (PBN). 3/4 range again. If you wish to call upon the traps and triceps more, than complete and lock overhead. Same as with the front press/push. PBN's also affect the front delts. Do not lower the bar too much. Touch the back of the neck/upper trap, never lower.
3) DB side press. Outstanding delt builder. Not to be confused with the regular DB press. One arm at a time, keeping the free arm holding on to something solid for support. A lot of weight can be used in this one hand version after awhile. Most guy's will handle around the 100 lb plus DB mark before they know it. Keep fingers forward on the DB and inline straight with the body.
4) High-Pulls, going as high as the lower pec/upper ribs (solar plexus about). Keeping the grip where you have a 90 degree angle between the upper arm and forearm at the top position. So this means a wide grip on the bar. This also affects the rear delts strongly.
5) Up-Right Rows. About a 10 to 12 inch grip. Keep the bar close to the body during the lift and pull to the upper chest. People have problems when allowing the bar to travel too far away from the body, which can produce too much stress on the shoulders themselves. With any pulling movement, it can affect the posterior delt head. This can be a outstanding exercise for the upper body when done correctly. Trouble is, most guy's do not do it correctly because of improper warm-ups and rushing the weight on the bar.
6) Power Lateral Raises. This is not your fathers lateral raise. This is the special heavy cheating version, where a lot of weight can be used on the DB's. Can be done one arm at a time or the two hand version. Start with the DB's in front of the body. Bend forward a bit and give a healthy heave ho, swinging them to about shoulder height. Try holding at that top position for a second and that lower. The elbows will be bent quite a bit during this exercise, allowing more involvement with the delts this way.
Pick two (3 sets each) or three (2 sets each) of the above exercises. With mass in mind, 6 to 9 reps. Hit the delts twice a week. Probably allowing 6 to 8 weeks on this type of heavy focused shoulder training. The posterior delts can be hit well with these pulling movements, as well as the cheat lateral raises.
Ask any Pro if partial and cheating rep's work (as suggested above) for mass. If he's honest you will get an overwhelming Yes. Good Luck.
