Literally, no. The US Census's collection of historical statistics on labour report that in the 1900 census, out of a total population of 51.4m, only 58.7%, or 27.6m, were in the labour force (series D 1-12, page 70) at all, people not in the labour force are not employed (nor are they "unemployed" per standard definitions), therefore 90% of Americans can't be right.
Let us give L Gold the respect of assuming that some context was lost and this is a claim about the % of the American labour force. It's still false, based on available data.
Series D 72-122 (page 74) shows the Major Occupation Group of the Economically Active Population by Sex. In 1900, out of about 29m gainful workers, most of them look to be employees. Some categories are unclear, e.g. "professional, technical and kindred workers" presumably includes self-employed lawyers, bankers, etc. But "Clerical and kindred workers", at 0.9m are unlikely to be self-employed (maybe an independent typist?) "Labourers, except farm and mine", at 3.6m, private household workers at 1.6m, farm labourers and foremen at 5.1 m (distinct from "farmers and farm managers"). Add those up and we're talking about 38% of the labour force already not being self-employed.
There's a much more detailed breakdown of occupation in the report in the following table if someone wants to go through and calculate a more sophisticated figure, but I think we can confidently dismiss the initial claim at this stage. (I do recommend a browse through the table, if you're interested in this question).
Note, the "gainful workers" in series D 72-122 is a different total to the "labour force" definition because it counted anyone who gave themselves an occupation from which they earned money "or its equivalent, or assisted in the production of marketable goods". So a retiree or an invalid might report their former line of work, or an employed student or a housewife might not as they regarded their paid work as temporary.
Just a note, in case of follow-up questions, I'm not an expert on US labour politics at this time (I can't even remember off the top of my head who the US President was in 1900), my interest is more in comparative economic development, which means I happen to both have a sense in my head of how the labour force in developed countries around 1900 broadly looked, and also know where to find these historical statistics.
Source
US Census, Historical Statistics of the United States, Colonial Times to 1957, available at https://www.census.gov/library/publications/1960/compendia/hist_stats_colonial-1957.html, particularly Chapter D, labour (pdf).
I feel like this question needs context for those not familiar with the game. Leo Gold is a character, a secessionist and terrorist, though a sympathetic one. He doesn't have to be factually accurate for his propaganda to make its point.