I've done a little bit of poking around to satisfy my own curiosity, and find that 2-stroke engines still are used some in marine applications and in Go-Kart racing. I don't find anything in the Go-Kart info as small as your generator, but some boat books seem to be still available(?).

An example:

Yamaha Outboards, 1992-98
(SELOC Publications Marine Manuals) (Paperback)
by Chilton Book Company (Author), Kevin M. G. Maher (Editor)

The description says:
"Covers all 2-250 Hp, 1 to 3-cylinder, V4 and V6, 2-stroke models, including fuel injected units. Also includes advanced oil injection and counter-rotating drive."

Comparable current engines that appear to be about like yours - and for which not manuals seem available - are rated slightly above the 2 hp minimum size indicated, so something at least very similar to yours might be included. I'm not familiar with the Chilton SELOC (marine) series books, although I've seen numerous fairly recent Chilton automotive books.

Once very useful, the newer Chilton auto books are 295 pp of boilerplate reproduced identically in all Chilton manuals from a 1943 edition, plus one or two pages of the same specs printed (per Federal Regulations) under the hood of any recent auto sold in the US, so they're seldom worth much; but the marine engine books might be better(?).

The book appears to available only as "used" but the prices quoted are mostly fairly low. Amazon is getting a reputation for advertising used books they don't have and can't get, but it might be worth exploring the possibilities as an "extended general curiosity" sort of thing.

I found at least one website that offers the SELOC manuals covering other years, but they want $40 (US) for a subscription to let you download and/or print "any pages you want for any one engine." I didn't save a URL (since I wasn't interested at that price - sorry) but you should be able to find it easily enough in the unlikely event you might want to.

Your particular engine draws a complete blank in all my web searches. Even "modern" ones in the same/similar size range are really rare.

John

John