What strikes me is that every single addition on there is correct. And there are quite a few of them, and some he would not have been able to get right without an understanding of place value.
There is:
10+60=70
7+6=13
70+13=83
20+2=22
2+2=4
22+4=26
3+93=96
Not a single mistake there. Clearly he can add.
But why can he do 70+13, (two-digit-number + two digit number, no bridging ten) in his head, without any 'working outs', and gets to the right answer, but when he is asked to do 22+22 (two-digit-number + two-digit-number, no bridging ten) he gets completely mired in a method?
This implies to me that it is really the method that is confusing him.
I am not sure that it is a lack of understanding of place value. If he didn't understand place value, he wouldn't be able to 13+70 in his head, I don't think. He needs at least an implicit understanding of place value for that, though maybe he doesn't have the words for it - doesn't get the terms 'tens' and 'ones' (or 'units').
It looks more like for some reason he doesn't understand how he is meant to decompose the numbers.
Perhaps he missed a crucial session, perhaps it was taught badly, perhaps he lacked the understanding of the words (tens, ones) to be able to follow the explanation.
What he seems to have taken away is that you have to take the digits and add them up separately, sometimes with a zero behind, sometimes not; then add the sums up for the total. What seems to have been lost is that you are meant to add those digits that represent 'ones' separately, and those that represent 'tens' separately (with the zeros).
If I were to work with this child, I would first establish if he understood the place value terminology. Then I would reinforce that, and practise decomposing numbers, by doing a series of exercises of the 341= 300+40+1 type, perhaps with the place value arrows and perhaps with lots of exercises where the numbers are displayed in a table with columns for hundreds, tens, ones.
It also seems to me that this child suffers from low confidence. He can add, as demonstrated in this worksheet. It would probably be beneficial to go right back to something he is good at and build up from there.
Calculator though does not make sense to me. It is after all not the actual calculations that he gets wrong; rather, he can't seem to be able to work out what he is meant to calculate.