There's really not enough info here to say anything for certain, other than vague "anxiety disorder" type of things (assuming here that it is a "disorder"), but a couple things come to my mind from what you do have here:
His own personality + what could be described as "hoverparenting" "Helicopter parenting" is a term often used to describe parents who are always doing things for their kids, instead of letting kids work things out for themselves. This can lead to kids being overly dependent on their parents for things that they should be capable of doing for their age (in your son's case, being in a room by himself), depending in part on the child's own personality (a naturally independent child is more likely to be capable, regardless, but a laid-back or conflict-avoidant child may develop co-dependence issues). While hoverparenting is caused by the parents' behavior, it's generally borne out of love and a desire to not see the child hurt or suffer. These are noble desires, but conflict and suffering are a part of life, and learning to deal with them start in early childhood.
If you find yourself doing things for your child that he should be able to do (resolving conflict with a peer, doing various chores, etc), take a step back and start teaching him how to do it, even if it takes longer and is more frustrating in the short term.
Autism Spectrum Disorder Again, without any more information, it's hard to say for sure, but several of the behaviors you've mentioned here point to the possibility of an Autism Spectrum Disorder. I'll explain why in a minute, but please note that Autism isn't just the stereotypical rocking in a corner and screaming at every touch, nor does it need to be an anchor on the rest of his life. Just because he's verbal, highly intelligent, or otherwise "normal," it doesn't necessarily rule it out.
Anxiety in general is a pretty prominent part of ASD, for a number of reasons. Have you ever asked him why he's afraid of being alone? This might help you understand why he's afraid. (If you notice what seems to be an abnormal amount of anxiety over a new or social situation, this may also indicate ASD.)
- Additionally, literalism is another prominent part. It's possible he has a hard time comprehending that the ghost stories aren't real, and thus, is afraid to be alone, or in a specific place that he heard a story about.
Being non-competitive isn't so much an ASD thing (though some tend to rationalize negative things), but it is possible that he's just not showing his feelings on the matter. Have you asked him how he felt about winning a specific game (after having won it)? Or, have you noticed a lack of expressed emotion in other aspects (not counting the rage you mention in a comment, I'll get to that one)? Have you asked why he's giving up?
What is he doing when in one of these "deep think" spells? Is it nearly always the same thing, such as drawing, or while on the computer? Also, do these spells frequently occur, say, after school or other social event? For people with ASD, these are often known as the person's "special interest." It's how they "recharge" or relieve stress, how they unwind. It can also consume all their time, maybe even requiring someone to intervene to get them to do things like eat or brush their teeth.
You mention in a comment that he gets extremely upset, even enraged, when embarrassed or reprimanded in public. Does this happen in private, too, or over things that you find minuscule and not worth getting that upset about? Do these outbursts seem disproportionate to the trigger? Have you been told by others that he's "making a scene"? Is there a pattern to when these outbursts are the worst (ie - toward the middle or end of a shopping trip, rather than at the beginning)? Also, what's the behavior that caused him to be reprimanded to begin with, and when does it usually occur?
Also, you mention that he loves playing with his sibling and seems quite caring with her. How about his peers? Does he have a lot of friends? How does he interact with them? Does he seem more aloof around his peers, or otherwise a loner? Social issues (particularly non-scripted social interactions) are a highlight of ASD, even at the highest levels. Kids on the spectrum tend to get along better with adults (because they have more patience for the child) and infants (because they're more simple beings and easier to understand).
Again, I'm not saying that he is on the spectrum, but what you've described here does point to it enough that I think it's worth looking into more, especially if you combine this information with what you have that you haven't told us. If nothing else, it's obvious he has some kind of issues with anxiety (separation or otherwise), given your point #1. In any case, it's probably a good idea to mention his behaviors to his doctor and even consider seeing a specialist, so that you can get him whatever help he needs to be able to handle his fears and anxiety. If nothing else, it will rule out disorders, and you can work on adjusting your parenting style to help him be more confident.