Well, first thing to note is the type of guitar, Strat, with single coils, pretty obvious but has a lot to do with the sound... also looks like he's got the pickup selector in the neck position... now, that isn't so common. A lot of players like to use the bridge position on the Strat because that sound really cuts through. But the neck position can sound really nice for lead when done right, as it is here.
He says in the description he's using a 30 watt tube amp, with just delay at the start. He doesn't say what kind of amp, but I'm guessing definitely a combo amp, not a stack. I really don't hear the delay until he kicks in the Tube Screamer.
The Tube Screamer "TS-9" was/is this green overdrive pedal that came out decades ago (late 70's, early 80's, anyone know?) and became a legendary classic, getting big prices on E-bay... Ibanez has since re-issued the Tube Screamer at a reasonable price, but you'll always get people swearing by the original ones.
It sounds like you're more interested in the opening sound. To me, other than that fact that the guy is really great player, the 90% of the tone has to do with the amp. Small, real tube amps sound great when driven like that, and I personally believe that the digital "amp simulators" just can't get that sound quite right. It always seems that things like Line 6 Pods can get great clean and super dirty sounds, but this "bluesy breakup" tone is the one that's really tough to mimic.
Kind of amps that fall into this category are Fender (tube amps) Mesa Boogie,
Hiwatt etc. These amps may well seem to be expensive and "limited" for the price you pay, but keep in mind they are designed to have a certain tone, and sound really really great in that one "sweet spot". I have a Laney Lionheart which cost $1000, all tube, British made, and I love it. It certainly is capable of producing the kind of tone you hear on the video. Adding an overdrive pedal broadens the amps sound quite a bit, but it tends to have a distinctive tone regardless of gain setting. So, with most of these amps, you'll either not really like it, or just totally love it. There's something to be said for having just a simple, really solid setup, like this guy's.