Domdaniel: <Penguin> Only really true in open games. In closed positions such as those that can result from the French, I've won games by leaving my King in the centre.
I could also offer more elevated examples. But yes, if you plan to open the game up - especially with Queens on the board - King safety is paramount. White goes wrong here with 9.Nxe4, both opening the game and forcing him to follow up with the horrible undeveloping move Ng1.
This is also an early example of the Semi-Slav, now a mainstay of GM play. In 1890, it had not been analyzed in detail, so perhaps the White Lasker (Berthold) thought his brother's play too passive, missing the counterpunching power of moves like ...e5.
His development system - Rc1 and queenside activity before castling - was known to be OK in the normal Queen's Gambit. If Berthold thought Black's structure less dangerous, he may have felt he could get away with an eccentricity of his own.
In fact, mainly due to White's tepid Bishop development on e2 and d2, Black is already better after the typical (Em) Lasker move 8...Ne4. White should just castle at that point, and suffer a little. Taking the Ne4 is a bad mistake.
Amusingly, if White tries to sac a pawn for freedom with 10.Ne5 -- avoiding the ugly Ng1 but letting Black win a pawn after 10...Nxe5 11.dxe5 Bxe5 -- Black doesn't have to accept. Instead, 10...Qg5! forces White to mess up his kingside anyway, with 11.g3, or 11.Bf1(!?).
I doubt if Berthold was very happy when he realized that, instead of castling, he was going to have to return a kingside piece (or two) back home.
A particularly amusing line is 10.Ng1 Qg5 11.Bf1, returning the entire kingside to its original quarters. But Emanuel avoided the aesthetic effect, and broke up the centre with ...e5. It's a little like a French Advance with colours reversed, where an undeveloped kingside isn't always fatal for Black. The big difference here is Black's 'extra' e-pawn.
There's something deeply pleasing in the way that Lasker Snr is forced to undevelop ... with the negative consequences you mentioned. And poor Bert had to play 15.Bf1 anyway, by which time he is quite lost.