So at the outset I should point out that the audiotape in question is a candid conversation between Hitler and the leader of an allied nation (Finland) whose support he desperately needed and yet which Mannerheim shrewdly refused to fully commit to giving. So given this context, you have to understand that Hitler is trying to lay out justifications for his actions, and the need to quash Russia. While Mannerheim is simultaneously trying to look interested and receptive to the man who may one day rule over all of Europe if Barbarossa is successful.

Now as for the Soviet's aims and ambitions. Certainly they had territorial goals focused on Eastern and Northern Europe, which were essentially revanchist Russian ambitions to at least recover the territories lost to Russia in the aftermath of World War One - you can see evidence of this in their botched Winter War with Finland, the annexation of Bessarabia/Moldova, the annexation of the Baltic States, and the willingness to dismember Poland in the Molotov-Ribbentrop Pact.

I can't say for certain that Stalin had concrete plans to launch a full-scale invasion of Eastern Europe, but if he did it likely wouldn't have been anything that grandiose. That said, a confrontation with Germany was likely inevitable in the long run because these two burgeoning powers were on exactly contradictory paths - Hitler wanted Lebensraum in the East, Stalin wanted to take back the Western reaches of the Tsarist Empire and also expand his influence into Eastern and Central Europe. So again, while in the audiotape we must treat Hitler's words with a little caution given the context and who he's talking to, I don't think it's unreasonable at all for Hitler to have actually believed the gist of what he was saying, nor can you fault him for that conclusion given Stalin's bullying behavior on the international scene, and the Soviet's constant military reforms and build-ups. Perhaps the most convincing point you could make is that this is a game that Hitler himself played adeptly - threatening and bullying his way into expanding his countries borders, revising the losses from World War One - and he simply recognized in Stalin another player at this game of his.

One last point that I think is interesting - the idea that Russia was getting too powerful was a strategic problem dating even back to the Kaiser's day, and may have contributed to World War One. There was a very real apprehension towards Russia's growing industrial power, and the simple Demographics in terms of Germany vs. Russia, in that the Germans understood that Russians already outnumbered them, and soon would outpace them in GDP and productive capacity and therefore become an unbeatable adversary.

In effect, this is an argument that Hitler is rehashing when he tells Mannerheim about discovering all of these tanks that Russia had been building up - an unbelievable number of armaments according to him.

Given Hitler's attitude towards Bolshevism as the irreconcilable enemy of his regime and ideology, and given Russian's military build-up, and fears of Russian expansion into the region, I don't think at all that Operation Barbarossa was unreasonably conceived.

Already by this point the Russians had reached that nightmare scenario where their GNP was more or less equal to the Germans, while having a larger population. Add this to the context of an apparent Soviet arms build up/equipment modernization, reorganization of their army, and aggressive foreign policy moves, is Hitler's supposition that a Russian attack on at least parts of Europe was coming an unreasonable one? I don't think so.

I believe that at the time, there was an impression that the gap between Germany and Russia was only growing larger every year. Such that you could say in 1941 when Germany was at the height (more or less) of its military preparedness and any delay would erode that preparedness. Conversely, the Soviets were still recovering from an officer purge and army reorganization so the Germans viewed 1941 as the best time to attack pre-emptively and win the knock-out blow that would curtail the Soviet menace.

In this sense, Barbarossa may be viewed as Germany's 'Pearl Harbor', and I don't think the comparison is totally invalid.

Edit: Thank you to /u/Georgy_K_Zhukov for reposting his answer. It's actually from a thread I made asking a similar question! As he says, the notion that the Soviets positively had plans to attack Eastern Europe is 'contentious'. In my above post I'm simply stating why Hitler would believe such a thing and how I feel that he's not irrational for doing so.

Barbarossa being a preemptive strike was certainly one of the justifications used by Nazi Germany when it was launched, but at best you can say the idea is very contentious. Certainly more that can be said on the matter, but for the moment I'll point you to this older answer I already wrote, addressing the "Icebreaker Theory", as this is sometimes referred to.