As per the title, this looks ideal for a short commute.

Many years ago I remember seeing several bikes with a small petrol engine driving the front wheel via the tyre

Yes bloke at work has he pays road tax etc

It's legal if it's registered, taxed and insured. A shop here used to sell the kits a few years ago but I never saw one done legitimately and the police crushed the ones that weren't road legal.

Why not do it with batteries instead.

Chap at work has one of those electric hub motors, but have a great stack of lithium batteries on a rack at the back. It is mental (illegal, but not many of the police will know the difference between an Amp and a Volt).

Look up ebike kits.

Legal and illegal ones out there

Isn't it just a form of moped, not a lot different to the old Raleigh Wisp (basically a shopper with a petrol engine)?

It would have to be registered, taxed, insured, tested, etc. if you wanted to (legally) use it on the road.

It is a moped, simples