He does tend to hang on to "I can't do it" feelings for long periods of time.
Help him feel successful - and to start with, don't bring up issues that leave him feeling Un-successful, like reading and writing. Some kids aren't ready to read until they're teenagers! It's not just *a* skill but something that involves coordinating several sets of skills and different people use different sets!
If he's feeling bad about not being ready to read and write, yet, it may be helpful for you to tell him all that, if you can do it in a way that projects a lot of confidence that these are things he Will learn, when he's ready.
But also help him find other ways to feel good about his abilities - what does he enjoy doing?
Oh, wait, you mentioned video games - that could be an avenue for highlighting the skills he has. It's Amazing that he can figure out games mostly without reading. It takes a Lot more thoughtfulness to work something out than to follow a set of instructions - but it could be he doesn't see that if he's been thinking "just video games". If you think of a game as a complex set of challenges in problem-solving, working your way through without the instructions is pretty impressive.
His letters are often backwards and he forgets to put spaces between words....I noticed that he memorizes the appearance of whole words, if that makes sense, as opposed to sounding or spelling them out and often guesses at words by the first few letters.
Those are fairly common traits of people who learn to read using "adult" skills which are more directed at observing the shapes of words quickly in a context of other shapes. Even people who learn to read by sounding-out transition to reading using more visual and contextual information than letter-sound information. If he's been *trying* to read by sounding out, he might be reassured to learn he doesn't have to do that - that sounding out is actually counter-productive (for him). It could (maybe, don't know) build his confidence to suggest that the trouble isn't that he's no good at reading, but has been taught to go about it the wrong way. So Any success in that regard is bigger - as an analogy, it's much, much harder to succeed in a video game if you're holding the controller upside down and backwards.
It's also possible he has some dyslexia, but I wouldn't jump on that right away. Some dyslexia is developmental and unschoolers with dyslexia don't tend to struggle to master it when they have confidence in their skill in other areas - its just another kind of puzzle to solve and not a big deal if they need to use some of the adult dyslexic tricks. The fact that he doesn't like to type suggests the letter reversal isn't as big an issue as his confidence.
He recently told me he has given up his plan to become an archeologist because he will never be able to read or write well enough.
It may help to let him know that he doesn't have to plan out his whole life right now, but that may have to do with subtle messages that he's been getting from you, too. If You've been worried that he won't be able to do this or that, it's likely you've communicated those worries to him in small ways. You may need to build up your own sense of confidence or trust in him. It could also be that you've (inadvertantly) put too much emphasis on "oh, you could be a..." rather than supporting him in what he loves right now. What have you been doing to support his love of archeology? I don't mean support his future entrance into a good college so he can become an archeologist but how have you fed his passion in the moment? If you've done a Lot to support it and he's had enough, that's fine! Passions don't have to last a lifetime or lead to careers, they can be transient.