Could someone please explain why this is a Jenkins bug?

Does it still occur on recent Jenkins versions and Windows versions?

In my opinion, it was a Jenkins bug, because it caused Jenkins to not start and Jenkins did not say why, causing much mystery quite often.
When Jenkins starts ok, it adds following events:

• envar JENKINS_HOME=...
• Starting ...\bin\java -Dhudson.lifecycle=hudson.lifecycle.WindowsServiceLifecycle -jar "...\jenkins.war"
• Service started successfully.

That said, it seems that Microsoft has understood the problem. Since Vista, the maximum event log size is bigger.
And I suppose that XP is not supported any more.

I checked the EventLogger class in .NET, it doesn't look like failure to log (assuming this isn't considered out of memory or otherwise fatal) should affect anything.

Is there a way to easily reproduce this? Write a tool that spams event log until it crashes, then try to start Jenkins installed as service?

I have reproduced this on XP with Jenkins v1.574.
After changing the properties of application events log to not overwrite (the default is to overwrite only events older than 7 days), the Jenkins service does not want to start and it does not say anything on why.
There is nothing written in jenkins.wrapper.log, jenkins.out.log or jenkins.err.log when this happens.

I'd like to reproduce this on a more recent Windows version so make sure this is still relevant in some way (even if much less likely to occur), is that the same strategy?

As I'm not regularly using Windows and would need to start a special Windows testing VM I doubt I have enough events to hit that limit (unless it's a real joke). Hence the question how to generate events.

I do not know how to generate windows applications events, but you can set a very low log size and no overwrite in the control panel:
http://technet.microsoft.com/fr-fr/library/cc722385%28v=ws.10%29.aspx

or create events:
http://stackoverflow.com/questions/446691/how-to-create-windows-eventlog-source-from-command-line

I reproduced the issue as described on Windows 8.1 generating the ~3000 events necessary for the 1MB log to stop accepting new events, and it caused a Jenkins service restart to fail.

Opened JENKINS_HOME, ordered files by modification date, and found in jenkins.wrapper.log:

2014-09-06 16:49:50 - Stop exception
Message:The event log file is full
Stacktrace:   at System.Diagnostics.EventLogInternal.InternalWriteEvent(UInt32 eventID, UInt16 category, EventLogEntryType type, String[] strings, Byte[] rawData, String currentMachineName)
   at System.Diagnostics.EventLogInternal.WriteEntry(String message, EventLogEntryType type, Int32 eventID, Int16 category, Byte[] rawData)
   at System.Diagnostics.EventLog.WriteEntry(String message)
   at winsw.WrapperService.LogEvent(String message)
   at winsw.WrapperService.StopIt()
   at winsw.WrapperService.OnStop()

Unfortunately it seems this is only added when stopping the service fails, not during the start.