I think "contributed to Hitler losing the Second World War" might be a bit of an exaggeration however he certainly didn't help. One of the major issues that is often shown as Mussolini hindering German war aims was the Italian invasion of Greece in late 1940.

The Italians invaded in October however by mid-December the Greek army had not only repulsed them but also were in control of half of Albania (which was under Italian control).

A counter offensive by Italy failed in 1941 after which the Germans joined in and eventually occupied Greece. There are arguments that this intervention ultimately delayed Operation Barbarossa (the invasion of the Soviet Union) and you can, (and people have) extrapolate the issues the Germans had in the Russian autumn in which the mud and unsuitable weather towards the end of the year slowed the campaign.

Here is a quote attributed to Adolf Hitler by Leni Riefenstahl (who made Triumph of the Will)

"if the Italians hadn't attacked Greece and needed our help, the war would have taken a different course. We could have anticipated the Russian cold by weeks and conquered Leningrad and Moscow. There would have been no Stalingrad"

The efficacy of this argument is debated however the official (at least in the UK) opinion is that the impact of the Battle of Greece was negligible to the plans of the Germans in regards to the invasion of Russia and that logistical concerns and previously wet winter played a greater role than Greece (Richter, Heinz. A (1998) Greece in Word War II)

Supposedly the German officers tried to quietly push the Italians into the British/French side before the war started. The English officers told their staff they wanted to keep the Italians neutral or on the German side.

Often the Soviets attacked the Italians and Romanian units as they were known not to be as well armed or dedicated at the Germans.