As the principal you always share some of the blame if your organization fails to reach its goal, but I'm not sure his dismissal would rectify the problems. There are plenty of problems at McLaren and not all are his faults. For starters for as long as I can remember McLaren hasn't got a top driver this year. Button is solid and dependable, but he isn't one who can make a difference. Checo is too inconsistent and prone to errors.
If there is someone who should be sacked it is whoever decided to ditch what effectively was the best car last season and go for a risky cleansheet design in a transition year.