But since the orbit of earth could still be approximated as a circle, that temperature change should be visible as some sort of sine wave, but it isn't. The graph shows a huge bump every 100000 years and not some harmonic wave.

If there was only one factor I agree that it would appear as a sine wave. However if there are multiple factors it would appear as more chaotic. Since there is a fairly high correlation between temperature and CO2 levels we can use the latter to extrapolate on the former.

Historically there is some event roughly every 100,000 years which is associated with a spike in CO2. Since historically there was a lag between temperature and CO2 it must be assumed that the temperature increase has a causal relationship. Most likely is that increased temperature has always caused increase volcanism, increased fires, increased methane release from polar regions etc. Since the last ice age, we have seen a repeat of dramatic increased temperatures and CO2. We have seen this dramatic rise over the last 20,000 years predating human technology. Indeed CO2 is a factor but it has only become evident in the last few years.

There is also a flaw in the interpretation of CO2 levels. The majority of the historical data is derived from sources such as the Vostok Ice Cores. The current level is obtained by observatories such as Mauna Loa.

Despite their assertions that the volcanic gases do not affect their collection I do not have confidence in the process. Even if they do have true levels, I have another concern about the interpretation of CO2 levels.

We assume that CO2 in previous time periods had certain levels because of the amount of the gas found in the layers. Currently we are not seeing new permanent layers being deposited. Each summer the layers previously deposited are being melted off. What if the same thing happened in previous cycles. The reason that we don't have a record of previous levels is that eventually the temperature reaches a point that the layers are melted away.

CO2 is also not the only factor in play. Water Vapour is another significant contributor to global warming.

Andrew Dessler and colleagues from Texas A&M University in College Station confirmed that the heat-amplifying effect of water vapor is potent enough to double the climate warming caused by increased levels of carbon dioxide in the atmosphere.
Source

The issue isn't that CO2 or H2O cause climate change, they trap the energy coming from the sun. If the sun is providing more energy, the system adapts to the new level. Over the last 200 years, we have been going through a solar maximum. The next solar minimum is due to start around 2020 in other words any day now. We have been so focussed on global warming, we haven't paid any thought to the potential of global cooling. A solar minimum is a short term event. However a mini ice age which is associated could last for about 400 years.