It appears that the LogEntries only processes the message text and not properties in the serilog entry so you are required to add the outputTemplate parameter to the LogEntries sink statement to handle any enriched properties that you use if you want them to show up in serilog furthermore, if you want them to be indexed by LogEntries you need to format them as key value pairs, KVP. I did something like this.
var log = new LoggerConfiguration().ReadFrom.AppSettings()
.Enrich.With(
new MachineNameEnricher(),
new ThreadIdEnricher()
).WriteTo.Logentries(
ConfigurationManager.AppSettings["LogentriesToken"],
outputTemplate: "{Timestamp:G} [{Level}] Mx={MachineName} (Td={ThreadId}) {Message}{NewLine}{Exception}"
).CreateLogger()