WI: a Genghis Khan like figure emerges in early 800s AD

  Interesting idea although I have some concerns.  Think your assuming not only that this guy is as skilled a leader as OTL Genghis but also that the region has the same capacity to produce a very powerful army and that he also has an many good generals working under him and for the next few decades.  If either of those assumptions were wrong then their going to be somewhat less of a threat.  However assuming both do occur.

1)  If so then yes the Tang are in a mess but there's no clear rival dynasty as in the OTL Mongol time and also Genghis only captured the northern part of China, which was weak and divided.  It was his grandson who conquered the bulk of China under the Sung dynasty largely by using Chinese forces from the north as infantry and with siege work.  The Tang are weak compared to the regional lords who have gained a lot of power but you could see a new unity emerge under such a threat.  I suspect that TTL's Mongols will still have problems with China. 

2)  The Abbasid Caliphate, although it had some troubles was at its height in the period 775-861 so the Mongols are going to meet it at its peak, which isn't going to be an easy battle.  Especially since the Mongols are pagans which would give opportunities for the Caliph to seek to unite his people against them.  That's going to be a much harder fight than against the divided and dilapidated caliphate in the 1250s. 

3)  Byzantium was weaker that the Abbasid's during this period although it fought regularly with them.  It was only in the 10th century that the empire had the ability to start pushing the Muslim's back.  The empire could be attacked by the Mongols one of three ways, from the north via either the Caucasus Mts or the Balkans or from the south east via Mesopotamia/Syria.  To get at it they however have to get through either the Khazars or the Abbasid.  Also the two eastern ones would requiring fighting through the mountains of eastern Anatolia, which with the theme system in place is not going to be easy. 

  The Khazar's are also about their peak in the 1st half of the 9th century and as steppe nomads themselves their going to be a challenge.  They are likely to go down if faced with a force as powerful as OTL Mongols but its not likely to be easy. 

4)  In terms of Europe its a lot weaker in this period with the collapse of Charlemagne's empire after his death and also the attacks of Vikings, Muslims and Magyar's.  However at the same time the bulk of eastern Europe is a lot less developed compared to a few centuries later.  There are more forests and swamps and those both make the region less attractive for conquest and also markedly more difficult for nomadic armies to maintain themselves.  Its noticeable that OTL Mongols had already partially withdrawn from Syria before the Mamluk's attack because they couldn't maintain their horses in the region and similarly despite military successes against Hungary and Poland they didn't manage to maintain themselves in the Pannonian plain.  Similarly with Russia while they briefly reached place like Moscow they didn't stay in the forests but relied on subject puppets while their Golden Horde descendants stayed in the steppes to their south, pretty much as the Khazars and others had done before them.

  As such I don't think the Mongols would get massively deeper into Europe then they did OTL.  With possibly weaker leaders and going against stronger opposition they might be stopped by the Khazars or the Abbasid or possibly even both.  If they do shatter the Caliphate it would hurt it more than OTL but unless the Mongols convert to a different religion than Islam their going to be largely absorbed politically and culturally.  Similarly while Buddhism, eastern Christianity and Zoroastrianism is stronger than in OTL Mongols period unless their very determined/skilled or very bloody in regards to the Muslim majorities across much of the Caliphate its going to struggle to maintain itself for any length of time.

  I think yes such an earlier Mongol empire could do a lot of damage to many countries.  However given the stronger opponents their likely to face they could fall short of OTL Mongol empire in terms of the territories they hold.  I definitely can't see them getting further into Europe than OTL. 

  Their likely to cause some drastic changes.  For instance assuming they get control of the western steppe its likely to butterfly the success of the Rus in establish states along the Dnieper valley region.  Central Asia, with less time to be Islamized could stay outside Muslim control for long or end up under another faith, especially if they did manage to shatter the Abbasid Caliphate and that could also slow the spread of Islam elsewhere.  Ditto with other differences in what people's survive or fail in TTL will change.