According to The Guardian:
Putin is likely to evade justice in the near future: Russia does not recognise the court’s jurisdiction, and insisted on Friday it was not affected by the warrants. But the Russian leader will face limits on his freedom of travel to the ICC’s 123 member states, further deepening his isolation.
And the BBC:
It is highly unlikely that much will come of the move - the ICC has no powers to arrest suspects, and can only exercise jurisdiction within its member countries - and Russia is not one of them. However it could affect the president in other ways, such as being unable to travel internationally.
But given that Putin possesses diplomatic immunity while traveling abroad... are his travels really restricted in any meaningful way? Obviously he can't show up in other countries uninvited but that was already the case before the ICC warrant. And if he is invited, he's covered by immunity and the warrant changes nothing.
So are Putin's travels now really restricted in any meaningful way compared to last week?