Two quotes:
"But let me say on this issue, if we got to know each other, you'd know the Pences love everybody," Pence continued. "We treat everybody the way we want to be treated. But on this issue, and it's frankly something that when the Obergefell decision was made which legalized same-sex marriage in America, the Supreme Court, Justice Kennedy wrote at the end, that this decision will likely create an intersection and tension between people in same-sex relationships and people in the exercise of their religious liberty."
"Look, I believe marriage is between a man and a woman, I believe in traditional marriage, and I believe marriage was ordained by God and instituted in the law, but we live in a pluralistic society, and the way we go forward, and the way we come together as a country united, I believe, is when we respect: Your right to believe and my right to believe what we believe," Pence said.
There's not exactly a specific law because it was decided by the Supreme Court. He'd most certainly support a law in Congress to overturn the Supreme Court decision though.
Your summary is certainly not about removing LBTG rights, it's saying he agrees with the institutions of the United States. I find it interesting however that that's how you'd choose to summarize the quotes.
The part about removing LGBT rights is where he's saying that law is / should be god's will implemented and that god's will is marriage being purely between a man and a woman. He can say he loves all equally, but he shows that's not true when he classifies some people's marriages as being unworthy of legal recognition.