Hi Dave
"Them" is Israel. It means, God put His Holy Spirit into the midst of the camp of Israel to guide the entire nation. As it was already noted in the OP.
"...."in the midst," "the inner part," or "among them". When applied to the camp of Israel, a collective group (which is what "within him" from
Isaiah 63:11 is speaking of), it's always translated "in the midst", or "among them". Remember, the singular suffix ("his") in
Isaiah 63:11 refers to the corporate body of Israel."
Taking His spirit from David does not necessitate the Holy Spirit indwelling.