LDS call it personal revelation. I think a better biblical term is illumination--so as not to confuse it with communication on the level of the universal Bible. I'm not sure, though, why you're surprised. Look at a broader swath of 1 Cor. 2:9-16--and I've highlighted other key verses besides vv. 15-16:
However, as it is written:
"No eye has seen,
no ear has heard,
no mind has conceived
what God has prepared for those who love him"—
but God has revealed it to us by his Spirit.
The Spirit searches all things, even the deep things of God. For who among men knows the thoughts of a man except the man's spirit within him? In the same way no one knows the thoughts of God except the Spirit of God. We have not received the spirit of the world but the Spirit who is from God, that we may understand what God has freely given us. This is what we speak, not in words taught us by human wisdom but in words taught by the Spirit, expressing spiritual truths in spiritual words. The man without the Spirit does not accept the things that come from the Spirit of God, for they are foolishness to him, and he cannot understand them, because they are spiritually discerned. The spiritual man makes judgments about all things, but he himself is not subject to any man's judgment:
"For who has known the mind of the Lord that he may instruct him?" But we have the mind of Christ.
That’s cool! I was always under the impression that classical Christians did not believe in modern revelation, i.e. communication of God to man. The Bible was it and all. I’m happy to be corrected! Thanks!