Does anyone know why this game ends in a draw:
Strange Draw

That is strange indeed. If white makes his last move, it connects 2 corner points and wins!?
Or is there some funny rule that when the board is full it means a draw?

Did you run out of time? Maybe what's happening is something like losing on time in chess when your opponent has only king and knight. You can't be mated, so even if you lose on time it is still a draw.

looks like software fault, game ends after move 37 when it should be 38

could be a error in a compare, e.g. > instead of >= etc.

Can't there be a restriction that the maximum allowed total number of moves is an even number?

FWIW it looks like a littlegolem bug to me. The rules of Havannah don't seem to make any special case out of filling the board or having only one space left or requiring the total number of moves be even, etc:

https://mindsports.nl/index.php/arena/havannah/49-havannah-rules

www.trmph.com predicted this outcome would be a draw, although I don't know why. Nonetheless, in tis one case, I feel like the outcome is correct. :-)

I asked Richard, and he told me it is a bug, but it seems he has no time to fix it.