"We love to watch people run a marathon."
Translation:Vi elsker at se folk løbe en maraton.
At kigge is used a little differently. I believe it would be more appropriate in an immediate/literal context, as in watching it/looking at it while it's happening. In that case it'd need a preposition, like "kigge på", as in, to look on. "At se" can be used habitually, as it is in this sentence.