I'm not as much on the Guly bandwagon as others, but the main thing he adds is versatility.
1) I am not sure why certain people think he doesn't hustle. Perhaps it is his languid style of movement. But Guly works hard and comes back to play defense. He is much better at this than either Lallana or Lambert (though they have their own strengths). He is also pretty tall and decent in the air. He does annoyingly duck out of headers from time to time, but he's still better in the air from midfield than Lallana, Puncheon and possibly Schneiderlin even. He's certainly not a great defender/tackler but he's good for an offensive player.
2) Guly is also possession-oriented. He passes backwards because often it is smart to pass backwards. He can be tricky with the ball, but in some of those tight midfield situations, it is better to simply pass to the open man instead of trying to dribble through two defenders. Just keep making open passes. It tires the opposing team out while giving your team a break, sparks confidence in the team and their ability to hold possession, and slows down the pace of the game when needed. Our midfielders often seem to have some difficulty with this. Cork and Schneiderlin always seem like they are going at 100%. Sometimes it's nice to feel like you're in control and relaxed.
3) Guly does the unexpected. He's probably the most likely player bar Lambert to just score or create a goal out of nowhere.
That is basically how Guly plays. He's good for a possession-oriented team that just holds the ball forever and lulls you to sleep before pulling some seizing a small opening to create a crazy goal out of nowhere. If you don't pay attention he looks like he doesn't do anything special as he's not as exciting with the ball as Puncheon, Lambert, or Lallana, and he's not as hard-nosed as Cork.
That is not how Saints play right now, however. Saints would probably like to be more possession-oriented than they are but presently don't quite have the players for it. Puncheon is very direct, and Lallana definitely likes to keep the ball moving forward, always looking for a through ball. And going forward Ramirez looks like he plays the same role as Guly only with more skill and flair.
For those reasons, Guly probably shouldn't start when everyone is healthy. But he should be a second half sub in almost any situation. If you need to hold a lead, take off an offensive player for Guly. if you need a goal, he could maybe replace one of the DM's.
Guly was solid against Stoke, and again today and I thought both games showcased what Guly brings to a side (though he should have done better on the missed goal). If you don't see it, then I guess he's just not your type of player.