Locked pawns in endgame where no progress can be made

I was reading about situations when it is vs isn't a draw when a side runs out of time. I was wondering what happens in this specific situation (included on the board in the post).

Is it a draw (in spite of there being "sufficient material") since there are no pawn moves and no way for either king to cross the centre in order to capture any pawns (which is the only way for either side to win)?

OTB, that's a draw. Here, it would be a loss for the side that ran out of time.

Laws of Chess:
"5.2.2
The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7."
https://handbook.fide.com/chapter/E012018 
So this position is a draw indeed.
The Laws of Chess are not correctly implemented on this site, because it is too hard to do so.
A human arbiter can easily verify that no series of legal moves leads to checkmate.
A program cannot yet do that.

Fair enough... that is what I thought too but wasn't sure since the game did not automatically end in a draw on the site when I loaded this position

I haven't experienced this but imagine if this position arises where each side has 10 minutes, but one has like 0.5s more. If both players are stubborn then you'd have to premove like 6000 moves (each premove taking 0.1s to execute) and just sit there till either side decides to leave or you waste 20 minutes collectively.

Some people will actually try to win such a position on the clock,  forcing you to make 50 moves before you're flagged.   This is why I ALWAYS play with increment. 

50 move rule.