Weird, my PC is about 7 years old and I haven't got any issues nor did any major upgrades since that time. I think the most intense part I played was when my screen was flooded with the flesh eating flowers and it was all fluent.
Haha no, I'm not playing these kinda games on my phone, but I can imagine a phone has slightly less processing power than a PC, so I can imagine it's lagging there indeed ;-) I don't think the Internet connection is the issues, as this is a locally played game as soon as it's downloaded, but there might be some online stuff happening on the background, don't know about that.