Can you do high interval intensity training simply running in place?

Technically yes, but actually running adds air friction making it a lot harder.

Running in place won’t ever provide an incline for resistance.

Maybe, but that sounds excrutiatingly boring.

Probably yes if you run harder but imagine just thumping your feet like crazy for 2 hours in a max 40X40 square centimeters sized area…

I’m with @lilikoi . I guess that if you ran in place hard enough for your interval, you could do it, but it seems that doing intervals of jump rope would be a lot less boring (and probably more intense).

Some people have said, they have created programs like this. I would suggest getting a decent piece of equipment. Some DVDs are also good.
I no longer have time for the gym; but I had gym training for years. I work out on my own. I have no need for socialization or the distractions. I believe if you understand how to exercise probably; who can create a program that works for you.

Sometimes I do high knees running in place for 30 seconds, then fall to a push up position then back up again and start over. Kind of like up downs in American Football, but you add more cardio by doing the high knees (you can also work on form as a sprinter).

You will feel it after 2 minutes, no matter how fit you are. (Just make sure the high knees are quick).