Try this code below. This should work for you. Let me know if you have any problems.
ClientContext context = new ClientContext("<Your Site URL>");
Web site = context.Web;
context.Load(site);
context.ExecuteQuery();
ListCreationInformation listCreationInfo;
List list;
listCreationInfo = new ListCreationInformation();
listCreationInfo.Title = "<Your Title>";
listCreationInfo.Description = "<Your Description>";
var listTemplate =
site.ListTemplates.First(listTemp => listTemp.Name == "<Your Template Name>");
listCreationInfo.TemplateFeatureId = listTemplate.FeatureId;
list = site.Lists.Add(listCreationInfo);
context.ExecuteQuery();
According to Microsoft: ListCreationInformation Elements
TemplateFeatureId = Gets or sets a value indicating the identifier of the function containing the list scheme for the new list
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