Just as the note tells you how long it should last, a rest tells you how long the silence is for. But that's the problem with a lot of tab. It doesn't actually tell you how long each note is. Ironically here it does say the rest is for one beat.
That's where real music scores (sic), and is added to good quality tab.
So, rests need to be 'played' in silence. To make that silence, mute the string after playing the previous note, by touching it gently with a finger, or palm, from either hand. Whichever is more convenient.
You're right - if the writer wanted that G or B to ring, he'd have written it as a minim (2 beat note). He didn't. Think of it like a trumpeter. Playing all those notes, but somewhere he has to breathe in for the next lot. That rest helps, and there's no sound while that happens!
Having said all that, there is plenty of guitar music - some very old, which has chordal playing but the chords are arpeggiated. Here, the notes are written out individually, and look like they need to each play for a specific short time. Do that, and the piece sounds stilted. What needs to happen is for each chord note to continue ringing. To write this on the stave gets to be, and look, complicated. So it's simplified. One has to listen to what's being played, and make a judgement. But for accuracy's sake, play any music exactly as writ.: that's (presumably) the way the composer wanted it. Rests and all.