Intel connection was not the sole reason for Nokia's demise in phones, but it contributed on the failure of their effort to recover from the tailspin. Symbian their old mobile platform was clearly due to be replaced and they had a pretty viable in-house Linux platform, Maemo, that already shipped with N900 in 2009. Instead of iterating on that, they decided to "join forces" with Intel and merged Maemo with Intel MobLin to create MeeGo. They wasted at least a year on that and not with a lot to show for it as the Intel chips they planned for never materialized.
Obviously it was going to be very difficult to compete as a third platform with the behemoths iOS and Android become during those years. At least the MeeGo and Windows Phone cards were not the winning ones.