Electric networks with an open-loop
I think that the lecturer uses an arbitrary definition of electric circuit. For many authors electric circuit is a synonym of electric network, this latter term being sometimes used for more complex circuits or circuits that are bigger in extent.

Unless he said something wrong, he is using a possibly non-standard definition, so you should ask him directly.

Maybe his statement was put in a context that may give a better understanding of what he meant, but if taken at face value, his statement is nonsense: KVL can be applied only if there are loops in a circuit. A network with no loop is a degenerate circuit, with no useful property.

Currents can circulate in a network only if there are closed loops, otherwise there is no current, hence no power transfer whatsoever.

Of course this assumes we are talking about basic circuit theory, where every network is assumed to be a lumped element network, and no electromagnetic phenomenon happens outside those little black boxes that we call components.

If we are talking about more general electrical "circuits", i.e. circuits where Maxwell's equations cannot be neglected, the same concept of circuit is somewhat blurry.