Tamerlane, more properly Timur Lenk, or Timur the Lame was indeed Muslim, having adopted the religion to make his rule a bit more acceptable to the Muslim states he subjugated in central asia.
Timur was essentially a terrorist as he would ruthlessly exterminate entire cities, ususally allowing a very fuew to live, maimed and sent off to nearby settlements to spread the fear. But he never made much attempt to hold territory or to rule it. It's hard to fathom what drove the man, but you have to conclude that he was a bloody minded maniac for starters.
The earlier, and far more successful, Mongols (Genghis Khan and his sons, for example) were by and large animists or Buddhists.
A really good book about these people is "Warriors of the Steppes" - can't remember the author's name...
Interestingly enough, Tamerlane got his full name from a accident (riding?) that left him lame. To accomplish what he did, as a 'lame' person, in his time as is nothing short of fantastic.
For some TUI (totally useless information) Tamerlane named one of his sons after the chess piece the rook. He also said their were only two activities worthy of a warrior, "Hunting and chess."
Finally, Belloc sounds a bit like an apologist for ISLAM and not an accurate historian.
RileyD, nwJ