B737-800 Captain reported a Critical Ground Conflict event during a cross runway departure. Flight crew stated spacing was dangerously inadequate spacing for a cross runway departure.

Narrative

We were cleared to land on Runway XX after being spaced 2 1/2 miles behind another aircraft. With this minimal clearance; Tower cleared another Company aircraft to take off on Runway XY for a cross runway departure. I'm used to this as I deal with it in ZZZ all the time. You can see the aircraft rolling and judge relatively quickly that your paths will not cross; that there is no real collision threat. In this case; it (no kidding) looked like we could be on a collision course; with both of us meeting at the runway intersection point. There was a pretty good crosswind and it's a performance critical runway on the best of days; so I had a lot to do.On top of all of that; I was worried that there may be an ATC mistake and was constantly thinking about what I was going to do if I went around. If he lifted off early; would there be a mid-air potential? If I continued and he didn't lift off; would there be a ground collision potential? Tower was busy telling the preceding aircraft to clear the runway; so the radio frequency wasn't clear. My First Officer (FO) and I were on the same page so he started giving me continuous updates on the departing aircraft; when it was rolling and how we looked. He ultimately said he thought we'd be okay; but it wasn't until 100 ft. that I saw the departing aircraft fill the windscreen as it rotated right in front of me. Honestly; this stuff scares the crap out of me. I've been flying here for 26 years and have seen a lot; I've got combat time as a Carrier Fighter Pilot; but this honestly scared me.