Usually!

As you correctly said earlier, g7 followed by Bg7 is the KID.

This move can herald a Nimzo-Indian, Bogo-Indian, or Modern Benoni. Or, you might find yourself back in a Queen's gambit line...

White could also play something like Nf3 oe e3 instead of d5, but in that case white foregoes the space advantage which goes with d5.

This line leads to an interesting clash of strategies. White generally builds a formidable centre and has prospects there and on the K-side. Black seeks to counter this with the combination of pressure down the e-file, possession of the dark long diagonal, and Q-side pawn majority. Black has chosen a very aggressive line. Tactics could explode at any time.

More usual is to exchange at once on d5, and then play ...d6.

I think 5...dxe6 is a playable line. But I reckon I would have stuck to what I know and played 5.e4 myself. Now if Black takes on d5, White can reply exd5, and Black doesn't get his Q-side majority. This looks to be reverting to a King's Indian, Old Indian or possibly a Czech Benoni system.

The Czech Benoni is solid and herd to break down. But it also promises little for Black in respect of counter play. Here's a Czech Benoni game from 7 years back: gameknot.com

I would have given ...Bg4 a good, hard look.

Yes ....Bg4 has been played here before, game 0-0 has also been played here, but I can't find Nb-d8 in any opening databases.

I prefer the pawn advance, myself!

I think he guessed my plan of g3-g4 and wanted to meet it with the check on h4.