Nope. He is writing about the church there.Peter is writing about Israel
1 Peter 2:5 Ye also, as lively stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ. 6 Wherefore also it is contained in the scripture, Behold, I lay in Sion a chief corner stone, elect, precious: and he that believeth on him shall not be confounded. 7 Unto you therefore which believe he is precious: but unto them which be disobedient, the stone which the builders disallowed, the same is made the head of the corner, 8 And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed. 9 But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light;
Notice here that same ones who Peter says are "a royal priesthood" he also says "are built up a spiritual house, an holy priesthood" and that spiritual house has Jesus Christ as its "chief corner stone". That is a description of the church similar to how Paul described the church here:
Ephesians 2:19 Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God; 20 And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone; 21 In whom all the building fitly framed together groweth unto an holy temple in the Lord: 22 In whom ye also are builded together for an habitation of God through the Spirit.