If Player A had a creature with shroud on the battlefield, and Player B cast Single Combat, would Player A be able to choose the shrouded creature as the creature they keep?
Yes, you can choose a shrouded permanent. And if a shrouded permanent isn't chosen, it must be sacrificed.
702.18a Shroud is a static ability. “Shroud” means “This permanent or player can’t be the target of spells or abilities.”
When a rule or ability uses a word with a rule meaning, it only refers to that specific meaning. Target is such a word.
Only the following target:
- Spells and abilities on the stack that use the word "target".
- Aura spells (since the rule text for these uses the word "target").
Keep in mind that certain keyword abilities represent abilities that use the word target (e.g. Equip).
Single Combat doesn't target, so it's unaffected by Shroud.
Yes. Player A may choose to keep - or sacrifice - the creature with Shroud.
Shroud is defined in CR 702.18:
Shroud is a static ability. “Shroud” means “This permanent or player can’t be the target of spells or abilities.”
"Target" has a very particular meaning in MTG. An entity is only a "target" when the card or ability specifically uses the word "target". Since Single Combat doesn't target anything, Shroud has no bearing on how this card plays out.